I've never heard of "hearing" a processor and if you can't hear the fan at all then something isn't right. I'm still convinced that what you think is the processor is really the hard drive you're hearing.
I'm on my second 11z with the i3 chip (swapped out the first) and the fan is quite noticeable in a quiet room on both. Both computer's fans behavior are identical.
And brookheather you are correct about the erroneous Atom info from me, the CPU I had in my old 11z was the Pentium Dual-Core SU4100. It's a Dual-Core though not a Core 2 Duo as you had mentioned. Confirmed that straight off Wiki's page on the Dell 11z 1110 (they never get anything wrong, lol).