I'm surprised that nobody mentioned that fact that another reason to use a heavy barrel is for greater stifness which translates into greater accuracy potential, and you don't need a super long tube either! Shorter heavy bbl rifles, are often more accurate, simply because they are stiffer! i.e., Remington 700LTR. In most cases minimal reductions in MV aren't of any consequence in real world applications.
As for the issue of barrel heat-up, I haven't really noticed any appreciable decline in accuracy under field conditions. From the bench you'll see vertical stringing, but nothing that really concerns me. Then again, I'm not shooting hundreds of rounds in an afternoon in the middle of a praire dog town either! Coyote hunting, you don't often fire more than a couple of rounds...if you do, you aren't hitting anything anyway!
I would suspect that a heavy fluted bull/varmint profile barrel (that has been cryogenically relieved of stress of course!) should heat up slower than a sporter weight barrel, while cooling at a comparable rate, due to increased surface are AND greater air flow over said surface area. Most varmint rifles with bull barrels are free floated with generous barrel channels that should permit greater air flow over the barrel surface compared to the average sporter rifle with pencil barrel and extremely tight barrel channels.
I'm no metallurgist or expert in thermodynamics, but I have observed the above under real field conditions. I like both, but tend to prefer heavy barrel rifles, whether it is my 700VS in .22-250 for coyotes or 700VS in .308Win or 700 Sendero in 7mm Rem Mag I use on Moose or Caribou. However, I don't feel I'm at a disadvantage toting my 700BDL in 7mm Rem Mag or 700 Classic in .223Rem.