Thats where the temp controller comes in - STC1000 or Sonoff, etc. Most all of them can turn OFF the exhaust fan when the heater is on, then turn it on again when the heater goes off.
If you insulate the tent, the heater wont have to run very long to heat up, then the heater shuts off and the fan turns on to bring in fresh air. As soon as the temp drops to the pre-set level, the fan turns off and the heater turns on again.
I have mine set to a temp range of about 6 deg or so IIRC. When the temp gets down to 72, the heater comes on and the fan goes off. Then when the temp gets up to 78, the heater turns OFF and the fan comes on.
It will cycle back and forth all the time during lights off.
During the ‘day’, the fan will stay on as long as the temps are up to 74 or higher.
If the tent is insulated, it will heat up fast and cool down slowly - other than the fan bringing in fresh, cold air.
So, yes, you will be heating the room, but I dont see any way around that. Insulating the tent will help, but you’re still going to be heating the basement no matter what.
The way the STC1000 works is you set a target temperature - say 75 deg. Then you set an offset value. I think Im using 3 deg. That means when the temp is below 75-3 = 72 deg, the heater comes on and it stays on until the temp reaches 75 deg and it shuts off. The “cool cycle” wont start unless the temp hits 75 + 3 - 78 deg. The fan will run until the temp drops back to 75 deg, but the heater wont come on until the temp drops another 3 deg to 72.
I have my temp sensor placed so that it is a ways away from the heater so there is some lag between its reading and when the heater shuts off. The temp always keeps climbing for a while after the heater shuts off as the air circulates inside the tent.
The short version - you set your desired temp - 75 in this case - and the STC1000 will allow the temp to fluctuate based on the offset valve, from 72 to 78 deg.
You can set any offset you want.
The better insulated the tent is, the less cycling you will have.