In short... I would not worry about it personally, especially given your on a laptop which typically runs hotter than desktops and not only that you reapplied the CPU thermal paste and I assume the fan it still working and getting decent airflow over the CPU. those temps don't sound anywhere near 'bad'. sure, they might not be 'perfect' but then again with a laptop in general I would expect to see noticeably higher temps than you would on a typical desktop.
Longer answer, which should give you a ball park estimate for temps...
I got a i5-3550 CPU (which I am running undervolted by -0.130v(which lowers CPU temp)) on my main PC with my room temp roughly 75-80f (maybe into the low 80's a bit) and here is some stats for me...
-Idle = 35-40c (I noticed this is probably closer to 35c when I got nothing running on Mint. but since I generally leave the Firefox web browser open for days/weeks etc, I noticed that there is always usually a mild load on the CPU cores, call it roughly around 10%, at which point the CPU 'idle' is closer to 40c (maybe a touch under). although when it's colder outside, like in winter, my room temp would be probably 66-68f or so at which point my CPU idle will decline further).
-Prime95 (AVX on (which is default Prime95 mode and generates maximum heat which is a 'worse-case-scenario')) = 75c, but generally 71-73c. room temp would have been about 75-80f.
-Prime95 (AVX off (which is more of a real world 100% CPU load test)) = 70c peak, but generally 67-69c. room temp would have been about 75-80f.
NOTE: my i5-3550 CPU is using my i3-2120 stock heatsink/fan combo which is not even the proper heatsink for it because the official i5 heatsinks have a copper contact that touches the CPU and goes into the usual aluminum heatsink. the i3-2120 stock heatsink/fan combo on the other hand is ALL aluminum, so cooling will probably be a bit worse I suspect. but... I undervolted the i5-3550 CPU by -0.130v which lowered my peak temps by about 13c at full load (so from the Prime95 info above you would have to add about 13c to those temps if I was running CPU at default voltage) which, while the stats I posted above are not 'optimal' they are probably still safe enough in general simply because I noticed, even on heavier tasks I do, that the CPU temps don't seem to go more than low 60's TOPS and are often in the 30's or 40's, maybe into the 50's occasionally, as to generally get into the 60c range (give or take) I got to be playing some video games which is probably the most demanding task I run in general even though if I do some lossy audio encoding (like FLAC to MP3/AAC etc) with Foobar2000 that can ramp up CPU temps to but since this does not really run for any length of time, even when temps come up a bit, it's not for all that long. but I imagine if someone encodes video that will tax the CPU pretty hard (not Prime95 level hard, but close enough
).
NOTE: those Prime95 tests were each run for 20 minutes(that Prime95 temp data was back from June 2020), which seems to be enough for CPU to peak and level off. so just knowing this, the tasks I do, even the more demanding tasks, are typically not going to have my CPU at 100% load for any length of time as even gaming, when as I was saying my temps might be as high as low 60's, the CPU load is not 100%, but it's definitely on the higher side of things.
NOTE: -0.130v is the most I can lower my i5-3550 CPU and for it to remain stable as any lower, like to -0.140v, while boots up etc, it does not last for all that long before the system will hardlock after maybe a day or two of uptime at the most off the top of my head. I can even go to -0.150v, which is basically THE max I can go and have system boot up as when I tried -0.160v the system had trouble booting/making it past BIOS screen. but at -0.130v, which is what I am currently using, I have reached 30-60 days of uptime or so without issue on Mint and it would have went longer had I not manually rebooted to apply updates. in fact, my record uptime is 68 days and 15 hrs. but I usually get 30-45days or so before some update comes along to where ill need to reboot, like a NVIDIA GPU driver update. because I noticed after a NVIDIA GPU driver update, while I can continue using the system, it seems to temporarily disable GPU accelerated x264 video playback (like when playing 720p/1080p x264 video etc through Celluloid+MPV (or SMPlayer etc)) until I reboot for the new driver to take effect and then GPU assisted x264 video playback is fine again and stays that way until I install a new NVIDIA driver update in the future.
but good news with unvervolting your CPU (although my guess is the OP can't adjust these things on a laptop) is that it's totally safe as the worst that will happen is your system will get unstable and hard lock, not from any damage to the computer, but simply because the motherboard is not supplying sufficient voltage to the CPU for it to run stable. but then you just power it off and back on and tweak voltage a bit higher until things stable out.
so while I don't think there is really any hardline data on what temps are bad for a CPU, I would think if your no more than around 60c in general, I personally would not worry about it at all, especially given under most typical use situations it won't see 60c or so anyways. even if it does, it's probably briefly, which I can't see doing much harm in the long term to the CPU. because, like I was saying, I would expect the laptop to die of random failure than from CPU death from heat alone.
looking up your i5-3320M CPU specs on Intel's website... it seems 105c is the max it can take as I suspect if it reaches this it will thermal throttle (i.e. CPU speed will slow down) to lower temps. even on my i5-3550 according to Linux's 'watch sensors' command it shows 85c for 'high' and 105c for 'critical'. so assuming this is a good ball park figure, I would not worry too much about running a CPU into the 60's. but beyond this it 'might' be pushing it a bit.
or another way to look at it... my guess is your laptop will randomly die before the CPU itself dies from heat issues. especially assuming you keep the airflow half way decent on it and it does not get packed full of dust.
bottom line... for me personally I would not even really be concerned 'at all' until 'at least' low-60's range and even that I am not all that worried, especially if it's not routinely in that temp range. although, speaking personally (since I don't think there is really any hard data on this stuff), I would rather avoid 70c+, especially if one is reaching that level of temp for any length of time. but this is on my DESKTOP setup, with a laptop I suspect even 70-80c probably ain't the end of the world, especially if it's not routinely in that temp range on your kind of CPU.
p.s. but between i5 vs i7, I would not really expect to see much temp differences. but going from a i5(quad core) back to a i3(dual core) you could expect to see a decent temp decline as was the case for me when I was running a i3-2120 as you could obviously see that runs noticeably cooler than my i5-3550 does when running at a higher load. like off the top of my head, when I was running that i3-2120 CPU with Prime95 topped out, I think the peak temps were low 60's(maybe mid-60's MAX) and that was with NO undervolting either as that was at stock CPU voltage my motherboard gives it. if I undervolted it, like I am with my i5-3550 CPU currently, it would likely shave off probably at least 5-10c from peak temps, maybe more.
side note: the OP can run Prime95 on Linux Mint through command line. but I would be careful to watch temps since they will go quite a bit higher than you see under typical usage/loads. here is Prime95 (64bit version), which will work on Linux Mint...
http://www.mersenne.org/ftp_root/gimps/ ... x64.tar.gz ; that's a bit newer than mine as I used "p95v298b6.linux64.tar.gz". basically just extract that file to say 'Prime95' folder, right click the 'Prime95' folder and select 'Open in Terminal', then run "./mprime" (without the ") and press enter than you can type in '15' and press enter, since we want to select the 'Torture Test' and then 'number of threads' should be '4' (since I assume you got a 4 core CPU) and then 'Choose a type of Torture test to run' you can select '1' or '2' or '3' or '4'. since we are primarily concerned with CPU temps here Option 1 or 2 is what we want. if your going for more of a worst case scenario use Option '2'. then on next thing it shows in terminal should be 'customize settings' which I just answer 'n' (which means 'no'), then on next thing shown in terminal should be 'run a weaker torture test (not recommended)' as you either answer 'n'(no) or 'y'(yes) as this determines whether Prime95 uses AVX ON or OFF. if it's ON it will generate more heat on CPU, but 'off' represents more of a real world CPU load at 100% and CPU will run a bit cooler here (but still plenty of heat as you can see on my own test). then finally it will say 'Accept the answers above?' and when you press 'y' and then press ENTER, Prime95 will start it's 'Torture Test' of your CPU and you will immediately see a rise in temps when you monitor it through 'watch sensors' and then it will slowly peak after some time passes (I would say by 20 minutes it will have probably peaked).
NOTE: you should be able to monitor CPU temps on Mint by opening another terminal window and do 'watch sensors' (without the ') and press enter. NOTE: to stop Prime95 or 'watch sensors' you just press CTRL+C and it will instantly stop. so if your running Prime95 and temps are getting too high for you to be comfortable with, just select that terminal window and then press CTRL+C and the Prime95 test will instantly stop and your temps will decline rapidly since there is no more load from Prime95. NOTE: I am not suggesting you use Prime95, but it's a good way to test CPU stability. I would say by about 20min the CPU temp will max out on Prime95.
p.s. on a side note in regards to Prime95... on my old PC (ASUS A8N32-SLI), it's CPU (AMD Athlon X2 3600+) does not even support AVX CPU instructions so you just run Prime95 with defaults basically. but on there my CPU temp, since it's dual core, seems to peak at 62c @ 2.4GHz @ 1.3375v to CPU. Prime95 peaks at 56c when running CPU at it's stock speed of 2.0Ghz and I undervolt CPU to 1.3v. the board seems to default to 1.4v which might be a little high since that CPU is officially rated for 1.35v