I'll bet you could "upgrade" your fan to achieve the operation you're wanting. All Fantastic Fans use the same motor and fan blade. Some are wired for exhaust only but replacing the switch allows it to reverse and draw air in. Everything is an option. The rain sensor is an option. I upgraded our older 6000A series to use a remote control. It will step the motor through 14 different speeds if I use the automatic setting. I can manually select any of those 14 speeds using the manual setting. It will turn off the fan motor in the automatic setting when it cools down but won't close the lid.
Fan-Tastic K6600R-417WH Remote Control Vent Upgrade Kit
I have another fan above my bed that works from a wall thermostat to open the lid and start the fan - the speed is selected by the 3 speed switch on the fan. It was exhaust only and I added the reserving switch so it can draw air in. It hasn't worked well from the thermostat - it short cycles and can't figure out if it should be running or not which causes the noisy gear motor to raise and lower the lid constantly. I push the thermostat to it's coolest setting so it runs continuously and if it gets too cool, I turn it off (works for me).
Fan-Tastic Vent upgrade kitsI think this is what you're looking for:
Fantastic Vent Upgrade kit 7350 Wireless Remote WhiteFeatures:
Hand-held remote for in-your-seat manipulation of vent speeds
13-speed manual mode
Thermostat actuated variable speed mode
Wall cradle
Automatic opening dome
Rain sensor allows your vent to close automatically
920 SCFM-High Speed
Amp draw is 0.2-1.9
Comes with wall cradle