as far as games i would recommend reading through some of the game threads. keep in mind that the tp2 runs wvga resolutions 800x480, therefore only certain games will run properly (full screen) on it. i use it for game but just not any that required directional buttons (yet). However there is a "keyboard controller" cab that can be installed on your phone that will allow you to map keyboard keys to any function, therefore you should be able to apply this to games.
here is list from a thread here about games that function in wvga properly:
http://forum.ppcgeeks.com/showthread.php?t=82849
there are plenty more threads concerning this issue as well. best advice is choose a game you want then search for its wvga compatibility.
I love this phone, very glad i switched to it. The battery life exceeds my expectations for a wm device, it is simply amazing. As far as heat goes, if you are referring to the tp's issue of getting rediculously hot when tethered or charging and using, then the answer is no, the tp2 does not have that issue. it may get warm or hot by definition to some, but it is not an issue and does not impeed on functionality, the issue was definitley fixed for the tp2. hope this info helps, and good luck