1) What model of HP laptop is it?
2) Does it have a dedicated graphics card? (re: switchable graphics)
4) What version of Mint? Both the desktop environment and the version number.
3) Try out TLP: www.webupd8.org/2013/04/improve-power-u ... fe-in.html
HP isn't really known for having good compatibility with Linux OS's. Or at least that was the case; might have improved.
Laptops with switchable graphics can reduce power consumption and thus heat by switching off the graphics card when not needed.
Desktop environments that are heavier on graphics, such as Cinnamon, will usually run hotter than those that don't, such as MATE and XFCE.