Make sure it has cooling. I know someone who has a laptop that overheats while web browsing. Try sticking it on some book and blowing a window fan on it or something, and see if you get your problem. I don't see why more ram would casue that bad of an overheating issue though.
To check your ram (which you should do regardless), download the ISO version of Memtest
and let it run overnight or longer (at least 12 hours) Make sure you have cooling during te test, I think it's liable to get hot. Andalso make sure your monitor doesn't burn in (As an LCD I don't think it can though).