That's bizzare.
I don't think it is heat because if your computer were overheating, you not have the ability to use ANY input devices (including your keyboard). Typically, if your computer is overheating, it will lock up and you would have to restart manually.
Also, I would rule out the possiblity of your PS/2 port or mouse connection being bad because this would totally freeze your computer as well... Including keyboard input. This also makes the mouse an unlikely suspect, but you might want to try a different mouse just in case.
The first thing I would try is using Safe Mode. If it fails to do it in Safe Mode, then you definitely have a software issue on your hands. If it continues to do it, then hardware is most likely to blame.. Or Windows itself.
How long do you wait for your mouse come out of its coma? The next time it freezes, just let the computer sit for 5 minutes and see if your mouse works again. I've seen a lot of problems like this where the person was just impatient and assumed it locked up. If the mouse becomes usable after a few minutes there is a software problem and it is probably fixable. Having an older, poor performing system can enhance this problem, usually.
To use safe mode, tap F8 a split second before the Windows 2000 screen pops up. A menu should appear with the Safe Mode with networking option... It isn't pretty, but it will be usable for typing and Internet access. Just use this for a few hours and see if you can reproduce the problem.