Wow, a 12v true heat gun would suck some serious current. Most 120v ones draw ~10-15A. That is between 1200 and 1800w. To get that power at 12v, you'll need 100-150A! The best you could hope for is to get a 12v hairdryer. Or, use a 120v extension cord (but make sure it uses 12-14GA wire because of the current).
You can get 12v tyre warmers with heated blankets for models (some with variable temprature) maybe 1 of those with 1 blanket wraped round the head and 1 around the crankcase would work without draining your battery so much, you could even use the other 2 blankets on your tyres.