Intel G620 has a TDP of 65W. I doubt your current PSU is up to the task, really. But how many amps are on the +12V of your itx PSU? Maybe it could handle a 35W TDP Celeron G440?
Intel's actually doing some sneaky tricks with that. Those 35W TDP numbers they give to the "low-power" versions are actually completely inaccurate. In reality, those versions only save you 5W at full load, and next to nothing at idle. Because of that, they actually give you the low-profile cooler on both the 65W and "35W" Pentiums. It's bad to go with the lower power versions because they lose a lot of efficiency due to their lower clock speeds and meager savings in power.
Stock coolers all Sandy Bridge Pentiums and Celerons come with:
OP, for the low cost Sandy Bridge CPUs neither the 'T' lower power versions nor the Pentiums are a good choice. Your 80W PSU will handle any Sandy Bridge Pentium even at full CPU+GPU load, but the Celerons are extremely close in performance to them and cost a good amount less. For example, the Celeron G530 costs $20 less than the Pentium G620 and should only be 6-7% slower on average. :thumbsup: