1151 Keyboard/Trackpad Locks, then Kernel Panics - after warming up?

Model A1151 MacBook Pro. All systems work fine at first - battery holds charge, machine boots, wireless connects, keyboard and trackpad work, USB works, keyboard backlight works... it can launch apps and connect to the internet.

However, a few minutes after boot - presumably once the machine has warmed up? - the keyboard and trackpad lock up. At this point the screen is still able to update in the background - web pages will load, progress indicators and clocks will update - but if left alone eventually the speakers will start making crackling noises and the system will kernel panic. (Due to "unresponsive processor") It will not reboot unless allowed to cool down (?) first.

If the machine is closed after the keyboard/trackpad lock and allowed to cool down, it WILL respond to an external USB mouse when woken up - and again the machine will function for a brief time - but the keyboard and trackpad do not revive without a reboot.

If it IS overheating, the machine doesn't seem to know - the fans don't speed up at any point during the lockup/panic process. Using SMCFanControl I verified that the fans do indeed work when activated manually.

Obviously I'd rather it be anything other than the logic board! But I'd rather not waste my time opening it up and smearing thermal paste on things if these symptoms indicate something worse.