>It's probably disapated enough that there isn't a threat of combustion from the hair dryer, right David?
I briefly considered verbally going down that rabbit trail, but I was posting 24 hours after the OP, so, yeah, although you can smell gasoline vapors down to a few parts per million, it has to be between 1.1% and 5% (volume/volume) to be explosive. All my cautions about getting the carpet too hot were for the sake of the carpet - not because of the small amount of gasoline. A glowing cigarette butt isn't enought to initiate a fire or explosion and the temps out the front of a hair dryer aren't enough either.
On the other hand, if you had VERY high concentrations of gasoline vapor, no, you shouldn't operate a hair dryer, (or cell phone, miniBic, flint&steel, wear synthetics, etc) because the nichrome wire inside is essentially a glow plug which any diesel engine demonstrates CAN ignite petroleum vapors (albeit preheated by an 18:1 compression ratio).