I am running Bitcoin-Qt, and it is shutting down my laptop while trying to synchronize. I even tried on a different laptop with the same result of shutting itself down.
This situation happens while synchronizing, the CPU usage and the CPU temperature raises dramatically and the computer doesn't have any other option than shutting itself down before becoming permanently damaged. How can I fix this problem?
I had something similar happen on a cheapie vps, bitcoin-qt is a demanding program, it crashes for you because it's verifying all the transactions that ever happened with bitcoin. To lessen the load, just find a torrent/download of the block chain. Also try out a thin-client (like electrum) if you only need basic wallet functionality.
It's normal for the cpu usage to increase, the client has a lot of work to do when synchronizing and verifying the block chain. The temperature should increase some but not dramatically, so you may have a cooling problem with your hardware. See if the same thing happens with other cpu intensive applications. If so, this is a hardware problem and nothing to do with Bitcoin.