Do the AMD's run a lot hotter ?
I don't know if this holds true with the latest processors from AMD, but at least some of the major series of AMD processors such as Athlons and Athlon XPs supposedly ran hotter. However, I think it's really not a big issue to most users; actually, I would say it's generally a non-issue.
Now, if you build systems using AMD processors, you had to be sure to properly apply thermal compound to the processor before mounting the heatsink, and be absolutely sure the fan is working when you first power on because AMD processors could quickly overheat and be damaged. Intel processors, on the other hand, would just throttle back and run slower if getting too hot.
So, as a practical matter, a properly installed AMD processor presents no heat concerns to the user. I bought a computer in Sept 2002 with an AMD Duron processor. I later replaced the motherboard and replaced the processor with an AMD Athlon XP 2200, which I'm currently using. I can tell from temperature readings that my processor runs fairly cool, ususally not higher than 45 degrees Centigrade, and often lower.