There's another thread around here where a member goes to great length to remove a heatsink from a CPU. I believe it was one of the older models, which used an actual adhesive pad, gluing the sink to the CPU.
If yours is like that, be prepared to fight with it (gently) -- let us know if yours is like this..

OTOH, if your machine is half-ways modern, and has a decent CPU in it, and real paste in between, it should be easy as pie, literally, to separate the two surfaces. There's no real "bond" formed by heat transfer paste; it's intention is just to fill in tiny imperfections & scratches in each surface, to provide a uniform heat-transfering contact between the two items. It is not glue (usually).

PS - Silicone, not silicon

Sasha

Oh--I thought it was silicon because one of the senior members used that word. Well, I guess the removal will be easy, then, because my machine is modern--I built it last summer.

Well, I just finished installing the new fan and reconnecting everything. I seem to have made it through the procedure without destroying the computer (or initiating the end of the universe). The thermal paste would seem to be working, because the CPU temperature is fluctuating between 25 and 27 C.