Can I run it without a CPU-fan, with just a heatsink?
Dont even try that... it will fry after a while. There is more silent coolers out there also, which still does a good job at cooling it down.
Though... if you underclock it and set it to lowest voltage... then it should work fine.. even my TB 1400 did if i clocked it down to 600mhz using lowest core voltage... i think it was 1.0-1.1 or something
And yeah... as EgonSpenglerUK said.. Via has some nice chips that run fine with just a small heatsink and they are cheap.. You get both miniatx motherboard with integreated audio, gfx, network for less than the price of a modern amd/intel cpu.