I have a sub-zero ice fishing tent which is the same size (or larger) than your shelter. I believe that you would need an 8000 BTU heater at a minimum - from my experience. I have an infrared propane heater attached to my propane tank. This year, I decided to buy a dual infrared propane heater from Home Cheapo for $119.00. It ia a 24,000 BTU device. I also bought a 5 lb propane tank for $45.00 from Home Hardware( this saves space in the sled).
There is a SAFETY ISSUE using these infrared heaters - they must be continuously monitored due to the fact that the heat surface is red hot.I had an incident where flame started travelling above the heater cone(I ended up turning the heater off and then back on to solve the problem). NEVER leave infrared heaters unattended.
Len