Since the mouse works on other computers, then the problem isn't the mouse itself. If the problem was due to heat then it would follow the mouse to other computers as well.
You don't say whether the freeze is while gaming or general computer use. If it's gaming use then I suspect a driver in the game for the mouse is the problem. And the fix would be either to reinstall that driver or the entire game.
If the mouse freezes during general computer use, then I'd suspect the driver that was installed for that mouse.
What I may next tell you may be wrong, since I no longer use XP, but go to Control Panel and look for the Mouse icon and make sure the driver for the mouse you use is still installed. If it is then the first thing you might try is to see if you can update the driver; I don't remember how it's done under XP. If the driver is missing, and a disk came with your mouse, then you can reinstall the driver from the disk. If on the other hand, the driver came from the vendors site, then you'll have to go to the vendor and find the correct driver for the mouse you have.
Please understand, what I have just said could be out in left field since I no longer use XP. But you have verified the mouse is good by using it on another computer. So look to your computer for the problem.