TODComp
First thing, the problem is not that your o.s is windows ME
Regardless of the predjudiced feelings of others
I am currently running a dual boot of Win XP/Win ME, and from years of experience that is not a symptom of a particular o.s.
The problem that you describe is typically a heat or power supply problem, that is assuming that you are doing routine system maintnance and are having no specific o.s related issues.
How long you had this system?
Have you opened the case, make sure the hsf is turning properly?
What about the psu vents, blocked?
You might consider a good dusting and checking for adequate cooling and ventilation.
When was the last fresh o.s install?
There are alot of different things that it could be, but its not win me just because its win me.