Your link says it's a mobile celeron. It's almost the same as a P3, but not quite. (Though all celerons are basically modified pentiums anyway. Modern celerons are just reject P4s.)
All of the Celeron's that Intel makes nowadays are aparently identical to the Pentium 3, and they all use the Coppermine core. There is one major difference, the Celeron has 128KB of cache. Intel's 733MHz mobile Celeron chips all have a 133MHz front side bus and 128KB of L2 cache identical to that in the Xbox. The chip inside the Xbox is the equivalent to that of a Mobile Celeron (the mobile Celeron has 8 way associative cache).
BTW: The Xbox processor had a 16 stage pipeline? That's rather surprising, as I thought the P3 architecture had a more normal number of pipelines unlike the insane P4s (20 stage pipelines, eek!). The Wikipedia article on the P3 talks about "instruction pipeline stalls" in the Coppermine, which seems to suggest a long pipeline too. Weird.
Um... I'm not sure, actually. I think it may have actually had 10 stage int and 16 stage fp pipelines, but I'm sure I remember reading at the time that the Xbox processor had a reduced size pipeline from the retail version, i.e. what I did wrote earlier.
But what I've been reading suggests the P3 was only ever 10 stages, which may mean I was talking out my arse

there. There was definately a pipeline modification made to the xbox version, though; there'd have to be the for new fp ops, I think.
That page I linked to, incidentally, was part of something I worked on for uni (although I worked on the Gamecube stuff -
here). So I'm pretty sure it's correct for the time, which was pre-release; IIRC the pipeline stage numbers for the xbox would have come from comparing them to the GC and absolute bastard that was the PS2 arch.
About the heat... As aldo already pointed out, it seems to be the PSU that's overheating, as people have been able to fix crashes by suspending the PSU in the air over a shoebox thus allowing greater heat dissapation. The console itself is very good about heat dissapation it seems with heat pipes and ventillation, though the fans are a bit loud (not as loud as the original Xbox however).
It's not 'very good about heat dissipation' if all it's done is move the overheating parts outside. That's like saying my Pc is very good at heat dissipation because I moved the motherboard to sit in the fridge. If the problem is actually this (rather large AFAIK) PSU, then that would strike me as a botch - especially if they put it outside the machine for exactly that purpose. It'd also be something very easy to test (if perhaps not to fix), and I can't help but wonder if they decided to rush the solution by just sticking it outside the machine, in order to meet the launch target.