Honestly you'd be fine with an Athlon XP with a decent cooler on it (IE, not the stock one). I had one with a water cooler and even on the hottest of days the thing at full tilt never rose above 40C, even overclocked as much as it was (1.6Ghz stock up to 2.0Ghz).
My Athlon64 runs at 26 Degrees (over clocked!) with the stock cooler, the one that came with the "Processor in a box".
I think the best thing about the Athlon64 is not it's 64bit ness but it's integrated dual channel memory controler... the performance boost that they alone give is phenominal!