ohgnomie Your laptop overheating could definitely cause these issues. I would suggest downloading hwinfo (it's free, and you can get the "portable" version if you don't want to install it) and running it while you play. Launch hwinfo, choose "sensors only," and leave it open in the background, then check the values once the game crashes or you're finished playing for the moment.
The app logs a lot of data, most of which is going to be irrelevant to you. So just look for the temperatures listed in the CPU and GPU (processor and graphics card) sections. Let me know what the max values are, and the current values if you happen to look at the app while the game is open. The CPU section will have a number of different readings, so you can just give me a range for the core readings.
The other useful step here is to scan the list of sensors to see if anything shows up red. If it does, even if it's just one max value in one category, let me know what category and what the value is.