I have an 05 Dr that has the same problem. I have not got into the carb yet, it is totally stock, but I think that is the culprit. Mine seems to miss and backfire when it is hot. Some of the backfires sound like a gunshot!
I ride at altitude here in Colorado, and suspect the stock jetting is the problem. Then again, what the hell do I know? Any advice from those that know bike mechanics would be appreciated.