
If there is enough heat coming from the CPU or other Board heatsink to make a USB hot, there are other, much more serious, issues.
OP, Did you make any recent changes to your system? New hardware, software update, settings? Generic mice require generic drivers, but if you have a specialty one it may require a specific driver (perhaps a recent software update requires the updated driver?).
Have you tried the mouse in a different USB port? While I completely disagree with #3 above, it is possible you simply have a USB port that is on it's way out. Try a different port and see if that works. You could also take a known-good USB device currently hooked up and move it to the port in question and see if the same thing happens after several hours - if it does, it's the USB port; if it doesn't, it's something related to the mouse.
Also, welcome to the Forum