I bought a used Dell D610 laptop a year ago and really like it. Since then I have purchased over 6 of them. Recently one of them started overheating and shutting down. Normally these laptops are a lot of work to get apart, but I figured out a quick 5 minute repair for this problem.
First remove the top cover plate by prying up on the right side and rocking it back and forth to disconnect it.
Next remove the 2 screws that hold down the keyboard. To remove the keyboard unhook the catch that is on each side of it then unplug it from the motherboard. The second screw is above the F4 key.
Next locate the screws that hold down the processor heat sink and loosen them. They stay attached to the heat sink.
When you remove the heat sink you should be able to see if it is clogged with dust like this one. Remove the dust and then put everything back together.
Be sure to check to see if the cooling fan runs on start up. It usually shuts off until it gets hot then it turns back on again automatically.