If you blow air into a wood stove with a heat gun trying to light things up it is going to blow a lot of smoke into the room. The air flow from the gun will exceed the air flow drawn out of the wood stove by chimney draft.
In the warm fall and late spring sometimes I have a problem having enough draft to light off the wood stove without smoking up the house. What I started playing around with this fall was using a heat gun to warm the chimney. What I do is build the wood pile in the wood stove with the larger pieces on the bottom. Then I place smaller pieces on top because I use the 'Top Down' method of fire starting. So, the stove is loaded but not lit, then I place a piece of cardboard in the door opening that has a tight fit. The cardboard has a round hole in it to accept the end of the heat gun. I run the heat gun for a couple of minutes to start a heated air flow up the chimney. Then I remove the cardboard and heat gun and light fire to the load in the wood stove. I pay special attention to the cardboard to make sure that it has not caught fire from the heat gun. This system had worked great the dozen times or so I used it this fall. Now that it is colder out I don't need the heat gun.
Some years ago I bought six Duraflame logs at a yard sale for a few dollars. I use a hammer and a wood chisel and knock off small pieces the size of a 25 cent piece( a quarter). This small piece of Duraflame log lights right off and gets the fire started really well. I'm probably using about 1/3 of a Duraflame log per heating season.
The 'Top Down' method of wood stove fire starting. If you are not using it, look into it. Been using it for over 20 years now and it works great.