Compile hmm? Not sure how to do that but it doesn't sound easy. As for a .deb file, maybe it's not such an easy matter either
Maybe you should try using liquorix kernels, more frequently updated and they have kernel 3.2, instructions here: http://r3dux.org/2011/09/how-to-install ... l-in-lmde/
Even better yet, I advice using smxi if you haven't done so already, go to http://smxi.org/
and find out how to install it. From there, you can enable the liquorix repositories and install the kernels safely
Dist-upgrading is also done nicely under smxi so you might want to check it out.
And if you really really want to compile your own kernel, take a look at this
LMDE (Release 1), tracking debian testing, Kernel 3.1.0-1-686-pae i686 (32 bit), MATE, Cinnamon & Gnome3
Plays (and rescues system) with experimental and sid repos on another partition, if grub boots nice that is.