Definately sounds like electrical temperature related, something is expanding with the heat, opening up, and interrupting power to either a coil or ignition part,have you checked the stator to make sure it is putting out good voltage when cold and warmed up (when its running)? Does it run fine right up until it quits, or does it start to miss and sputter before it dies? I had an older sled that did the same thing, started and idled great cold, take it out for a run, it would just die, turned out one of the coils was dropping out when the motor warmed it up, put 2 new coils on it and it ran like a champ.
2000 Indy 500 XC, Fox shocks up front, M10 trail in back. '99 440 XCR for my son. 96 XCR 600 SP tripple pipe, 862 miles on it !! (until it snows....then look out, odometer !!)