Radiant heaters aren't really designed to cycle on and off repeatedly, so an additional temp controller wouldn't do anything extra special.
The stock thermostat should be fine. Suppose you could mod it and relocate the sensor if you wanted, but the fans your talking about would circulate air through it anyway right?.
Mine has like 3 settings, and I usually keep it on the lowest (600w?).
You can stuff it in the tent but there isn't a point in that either, especially if your venting directly into the room. It wouldn't matter where it is in the room, next to the tent or whatever. It will heat everything the same.
If venting completely out of the tent and room, the fan will just suck the heat right off the heater, and waste all the heat (unless you have a heat recovery ventilator)
I've had my eye on the cheaper on demand electric radiant flooring kits lately.. Small sections too, perfect for tents. Made to be covered in thin set and tiles. I would use my own temp controller, and make a 4.5' x 4.5' heated panel with elegant looking tiles (and added side wall splashes) to set in my tent floor. Best heating system I can think of really...
That, or use a coil of pex tubing and coolant instead to make the radiant floor heat panel, and a $100+ portable on demand propane water heater to heat it with. A closed loop system with its own pump, which is what signals it to turn on with pressure. Hook temp control to pump, easy peasy. At the same time, you seal the room off, and you get your c02 from the same units exhaust! Sounds like a win but I haven't attempted it yet, lol..
I would also toss an aquarium heater in the res, preferably a shatter proof one. I always have too in the cold months. Digital temp controllers work great with them to keep your res temp dialed in. You don't have to worry about the canopy\ambient air temps so much when you heat the res at night. Bonus if you want to bring out fall colors during the cold season.