How much time can a normal home CPU run before it heats up badly and gets damaged?
In normal operating conditions your more likely to outgrow the cpu than have it go bad on you. I would say you should be more worried about your hard drive going bad because of all the moving parts.
Do you mean ... without a heatsink and fan?
Pentium, I don't know, but I wouldn't suggest trying it.
Athlon, I'd say it's life would be less than a minute, maybe much less. I once had a tab break off a cpu socket so the heatsink & fan just popped off. I just heard a loud snap & while I was sitting there wondering what caused the noise -- maybe 20 or 30 seconds -- luckily the system shut itself down before the cpu (an Athlon Thunderbird) fried. The thermal compound had already liquified, run off the top of the core & baked onto the surface around it. I was amazed when I found that the thing still worked.
An athlon processor will last aprox. 12-17 seconds without a heatsink. Pentium will last a little longer. I would say aprox. 30-50 seconds. But with everything in place these processors will run for a long time. I still have a 300mghz pentium 2 that I use as backup storage and she is running strong.
also if you have just a factory fan and you overclock your cpu you run risk of overheating it that way
Separate names with a comma.