I have never heard of instability due to heat, if you have good cooling the CPU shouldn't heat up that much, The Pentium 4 makes a lot of heat too, all current CPU's, with exception of the VIA C3 Ezra, CPU cooling shouldn't be an issue unless you want to overclock it, which seems like a waste. I say, if you have good cooling (which for such a pricey chip you really should) go for it. I don't know why that shop says the Athlon 64 gets unstable with the heat, since Tom's Hardware has NEVER to my knowledge said anything about in-stabilty. They say the chip runs HOT but they don't say it runs HOT to the extent of being instable, and AMD to my knowledge has released anything talking about heat instablity. No one on Newegg in their reviews have ever said anything about Heat being an issue, the shop may just want you to buy the Penitum 4 3.2 because they make more money on it, or they just don't like A64. There are no 64-Bit applications out there yet, but there are applications that can benifit from other things with the Athlon 64 (This was an article written about Dual Opteron 64 processors, with lots of professional software) but for music editing the A64 is supposedly the best, since it isn't limited by RAM or a FSB (the FSB thing I was sort of unsure on, since I thought it was just a 1600MHZ FSB or higher) But anyways you can find the article in the August editon of CPU Magazine, about the DAW workstations ( I am guessing CPU Magazine has a website, what it's URL is I have no idea)
But for a good buy get the AthlonXP, buy the best one you can afford (the XP 2700+ is a good model, so is the 3000) or the one that best fits your needs. About 50% of THG's benchmarks are done on the AthlonXP 2700+ with varying graphics cards (they do a lot of GPU benches with the 2700, either the 2700 or a 3.2GHZ Intel, but the 3.2GHZ what they used on VGA Charts III)
I have never had CPU power loss with my AthlonXP 2600+ (the older non-barton T-bred B one, with the 266MHZ bus, so it runs faster than almost any other 2600, 2.14GHZ compared to 1.9GHZ) I am very happy with AMD, I run my CPU at 47-51 Celcius, but I don't think the A64 would run much warmer (if you get a good cooler that is, I don't have anything special on mine BTW, just basic about 1 step above stock i'm guessing) Since I am AMD biased I would suggest the AthlonXP, but Intel's Penitum 4 2.4GHZ and 2.6GHZ models aren't bad either (they perform in-line with mine, the 2.6 is slightly above since mine is designed to perform like the older P4 2.53GHZ) I wouldn't buy the latest and greatest unless you need it, since it won't be the latest and greatest in 8 months.
I again would buy AMD, IMO.