Yes, I am aware that a heating element/coil is used in an electric hair dryer.
The space inside a fuel tank has massive potential for explosion - because the air-fuel ratio (not the liquid fuel) is within the range where those vapors will easily ignite. If you opened your fuel door, unscrewed your gas cap, and dropped an open flame ignition source like a match into the filler tube, you have a very good chance of blowing yourself up - real good. (Props to John Candy).
If that same level of concentrated gasoline vapor was floating around in your garage, you'd have a serious leak combined with poor ventilation such that 1) You'd smell it immediately, and 2) You'd better not have a furnace with a pilot light, because your day is about to take a turn for the worse.
I use electric heaters in my garage (with fully exposed heating elements) continually throughout the winter - as well as my trusty hair dryer for various other purposes like heat shrinking insulation on soldered wires. Millions of other people do as well. I normally have two (gasoline powered) cars in that garage, as well as portable gasoline containers used to refuel yard equipment.
I maintain, the biggest risk of using a hair dryer to warm your exterior fuel door is damaging the paint, from over-zealous application.