Again. Nonsense. Heat is not the issue, but power and temperature cycling. Do some research.
Heat (ie transfer of energy) and temperature nominal are very small considerations compared to activation energy and thermal cycling. You could run a CPU at a higher temperature constant and it would last longer than a lower temperature cycled. Research Arrhenius equation and compare it to an acceleration curve (Coffin-Manson equation).
Heat is
an issue. If you don't believe me, replace your heatsink with a fanless low profile one. Don't worry, it won't reach the temperature where the chip shuts itself off, it'll be a comfortable 70C or so. But that's okay, because you're not overclocking it, right? So heat won't be a concern... [/sarcasm]
Your equations are irrelevant to this situation. They're neat... but irrelevant.
The Coffin-Manson equation is an equation from the 1950's characterizing cracks in macro-scale metal, chiefly solder joints. We're not talking about solder joints here, boards barely have any (if any) solder joints on them considering most of the components are IC's. That equation is not designed to hold up at the micro or nano scale.
oh wait, what's this...? Oh! I found the page that oke was looking at:
http://www.ami.ac.uk/courses/topics/0163_ettf/
Odd, it agrees with me!
"As the peak temperature increases, the number of cycles to failure reduces very markedly " - Peak temp increases, lifetime decreases
"As the temperature range of the cycle increases, the number of cycles to failure will decrease rapidly." - Wider range of temperatures, consistent with weak cooling, causes lifetime decrease
"You could run a CPU at a higher temperature constant and it would last longer than a lower temperature cycled."
I could what? A constant is a constant, it's consistent with the materials used. It doesn't change if you change the temperature.