One important piece of information which you need to consider would be the difference in pressure between the two rooms, the split room design is good but it's hard to work with when it comes to air pressure, I don't know the exact setup of your farm but if I understood you correctly I believe you might have to increase the exhaust and reduce the intake.

One way to confirm this would be making a small hole in the outside wall of the hot room, and then place a piece of paper on it (from the inside), if the hole sucks the paper then you are good, if the paper is pushed to the inside (which is what I believe to be the case) then you need to balance the pressure.