ooof. That's unfortunately common with the newer radio systems. The cheaper way (I think) would be to disassemble the radio and rewire the fan to an accessory line in the car, like the cigarette lighter, so it only turns on when the car is on. A competent audio shop might be able to do that for you, to the tune of $~150 in labor. Have them ensure it's a 12 volt fan, if it's lower power you might need to have a voltage regulator. Again, a good audio shop should be able to take care of that.

As is, a small 40 mm fan won't kill your battery if it's a daily driver.