Most likely, heat probably is not the issue.
I could make a snide comment that Windows ME is the issue, but I won't 
Most systems, even ones old enough to be running ME, usually have a thermal protection feature that shuts the system down in the event of overheating. If your system was running too hot, then it would not have frozen-- it would have either shutdown, or you'd see smoke eminating from your PC! :o
I'd try starting in Safe Mode, and seeing if you can even get in from there. When the computer is booting, just before Windows loads, you either hold down the Ctrl key or the F8 key, and you'll be presented with a menu to enter into safe mode with.
Have you run a spyware or an antivirus scan lately? I'd suspect that, more than anything... Also, did you get any error messages, other than the bluescreens?
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