Is it insane to replace a CPU without replacing the heatsink?

"The new processor will generate more heat than your old one, so you will need more cooling than before.

Given the new processor has come with a big fan it would suggest it needs that level of cooling.

If you just use the heat-sink then the best you can hope for is that the temperature monitoring system will kick in and shut the CPU down to protect it. The worst case is that it will cause some heat damage."

"You can do this, as long as you make sure:

The heatsink is sufficient for the thermal output of the new chip. A celeron M has a lower heat output than a dual core, so this is dubious - if you're talking about the stock heatsink that came with the celeron on a pentium dual core then you may want to reconsider.
You replace the thermal interface material (thermal paste). This is absolutely essential as without it the heat won't be transferred correctly.

Most heatsinks that are bundled with CPUs come with thermal paste already applied in the form of a rubbery pad that just gets squished between the CPU and heatsink. However it is also possible to buy thermal paste in a tube, which is liquid rather than a rubbery pad. If you remove the heatsink and re-apply it, it is a good idea to scrape off any thermal paste whether it be a pad or liquid, and clean the cpu and heatsink with alcohol, removing traces of it. Then, making sure there is no dust or foreign objects on either surface, coat the top of the CPU in a thin layer of new thermal paste and fasten the heatsink down onto that. Follow the CPU manufacturer and thermal paste manufacturer's directions.

If there is already thermal paste on the heatsink in the form of a pad and it's more or less intact, you may get away with putting it back down on the same CPU (although I would advise it's a bad idea). But when changing CPUs always replace the paste."