Most modern cookers are designed to burn clean when there is a pan on the supports. Attempting to heat your tent with one is not a good idea. You might want to look at portable heaters.
I'd suggest hookup plus normal fan heater with variable thermostat.......used to use this all of the time, warms up the tent quickly and can leave it on overnight.
Interestingly, on another thread about fumes, it was quoted, that with pots on the cooker, ten times more fumes were created. I think it was a trangia stove army test
------------- Canvas tent, paraffin light, petrol stove. Heaven
I'd rather be kayaking.
Spent up, not pent up, just had my new tent up.