Both are based on the 65nm process
The 4400s TDP is 65W and the 6600s is listed as 95W
The thermal specification of the 4400 is 61.4C while the 6600 is 71C
So, all in all, as the Q6600 can go up to 71C I think the E4400 HSF should cope.
Just keep an eye on the temp when you first switch on the PC. The quickest way to do this is via the BIOS.