Will: Just noticed the indoor temp threshold requirement. Resubmission below:
Put a J thermocouple outside, a second one inside. Connect their negative wires together. Connect the other two ends to an ON/OFF temperature controller ranged for 0 - say 100 deg C with the cold junction compensation disabled. Some controllers offer this feature. Put the set point to near zero (= the indoor/outdoor temp difference at which the fan has to come on)
Use a cheap wall thermostat set to the indoor temp below which you don't need cool air coming in. Connect its contacts to inhibit the fan when the thermostat shows "cool enough".
You will have to play around with or work out which of the two + wires go to the controller's + terminal. And which thermostat contacts to use - N/O or N/C.