You are correct that the Xeon supports both 32 and 64 bit applications, but I have yet to see any Xeons retailed anywhere, and from what I've heard, they are far more expensive than the Athlon 64s...
I've run two athlons and a duron, and I'm not afraid they are going to melt away. Also I would think that if melting was that severe of an issue the 64s would not be recieving the praise that they have.
By the way, I run a Pentium 4 and I absolutely love it to death, runs great, but as far as the benchmarks say, the 64s are superior to P4s, and I haven't seen you bring up any argument that says otherwise yet.
Intel C2D E6320 / AMD Athlon X2 3800+
Gigabyte 965P DS3 / DFI nF4 Ultra-D
2GB OCZ Gold PC2-6400 / 2GB OCZ Gold PC4000
eVGA 8800GTS 320MB / eVGA 6800GS 256MB
150GB Raptor / 74GB Raptor
2x500GB / 320GB
OCZ GameXStreme 850w / OCZ StealthXStream 600w