Awesome post. Who was the cranky researcher who developed the climate-controlled window system with the Linux box and python scripts? I want to do the same thing.
Same, but it seems overkill. I'm in an old office where the only openable window is consumed by a window A/C unit. I want to put a 120mm fan in a small opening next to it that'll turn on when it's more than 3C cooler outside, and more than 24C inside. Seems like an Arduino would do it.
It could be much simpler.
If I understood the problem, a differential amplifier (any opamp would do) wired to the temp sensors would output a voltage proportional to the difference between the two temperatures, plus adjustment. This voltage then can be used to drive a pwm generator wired to a h-bridge that drives a reversible fan that would pump air with speed and direction depending on the difference between two temperatures, so that it could be used both ways too warm up or cool down.
The same could also be done the digital way by using for example an uber cheapo ATTiny85 small board wired to the sensors, plus the fan and its driver, then doing all in software. That little critter has just the right amount of ports for the job and then some.
Not checked on paper (especially the first) but on principle both should work and also would be extremely cheap.