I was originally thinking about using a small actuator but I don't know too much about electronics so I was trying to keep it simple. I wanted to use the power that is sent to the fan and it seemed like an actuator would need something to tell it to open and close. I ended up getting an electromagnet ( magnet with 2 leads coming out). It is 12v dc .33 amps and has 25 lbs of pulling force. I believe my fan also pulls .33 amps so I figure it should work because digiq supplies 2 amps.
I have a simple plan that will hopefully work. I'll have to post pics cuz I'm not using the BBQ guru fan, I made my own. I basically wanted to build the drafts door inside a 3x3 square tube only 3-4 inches long. It will simply have a hinged door hanging from the top with extra weight at the bottom. The magnet will be mounted on the top of the tubing and wired Into the fan. This way when the fan has power it will also power the magnet pulling the door up out of the way ( the air will also aid in blowing the door up out of the way). Once the fan is off the fan will swing down in place preventing the draft.
The only possible problem I see is that because the fan "pulses" it may affect the performance of the magnet. I think that the pull strength of the magnet (25 lbs) should be no problem for the very light door and the airflow will keep it up. Let me know what you guys think