Shooting out of window cold weather

I have a shooting shed that I shoot bench rest out of at up to 110 yards. In cold weather, anything below 50 degrees I heat the shed to around 75 degrees since I usually shoot for a couple of hours. This causes a mirage through my scope since the length of the barrel is inside the 75 degree heat and the air out side the window may be only 40 degrees or down to the 20's. The colder the weather the worse the mirage is. Anyone else have this problem and how to cure it.
 
I shoot out of our bedroom window when it gets cold.
It helps reduce mirage if I turn on the bathroom fan to reduce the amount the amount of warm air going out the window.
I also shoot from a spare bedroom window. The mirage can be managed some by reducing the size of the opening. I use 2” styrofoam to cover the open window with a 6”x10” section cut out to shoot thru. This also helps keep the room at a comfortable temperature. Uj
 
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