Is the heatsink from the core 2 able to fit the socket configuration on the Pentium 4 mob?
If the pentium 4 mobo has a socket 775 processor the core 2 heatsink should fit, as for cooling capacity the core 2 heatsink should be able to handle anything the older p4 could throw at it.
If the p4 mobo is a 478 pin you are SOL unfortunately, some smaller computer stores will give you a partial trade which might be worth looking into if the 775 heatsink doesnt work.
Here is a picture of a 478 heatsink retention module (its upsidedown)