I deal with Compaq laptops alot and haven't seen many cases of them shutting down from over-heating. Laptops are alot different from desktops though in terms of space and the ability to have proper ventilation in them. With so many components packed into a limited space, it's hard to get proper air flow in a laptop. Your overheating problems may be caused by the CPU being hot from the 100% CPU utilization and the laptop's inability to properly cycle out the hot air out of the laptop and get cool air into it. I suspect this may be the cause of your problems, especially if it doesn't happen during regular use (non-OOTP usage).
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