Thanks Maki2, I should have included the Olympian Catalytic heaters in my recommendations, but I was mainly trying to stay on the topic of wall-mount LP blue flame heaters with thermostats and their 'cousins', the ones with manual controls.
The largest Olympian Wave Catalytic is 8000 btu, and has no thermostat, whereas the typical blue flame LP heater is 10,000 btu (and up) and available with a hydraulic, built-in thermostat. Olympian Wave heaters typically put out less (near zero) carbon monoxide, so they are much safer if the occupant will be sleeping with the heater in operation.
Other than btu input/output and features, another difference between the two different styles is price. A typical wall-mount 10,000 btu blue flame or infrared LP heater can be bought for around $100, whereas the 8000 btu Olympian Wave 8 Catalytic heater is around $300 to $350.
Having used them both, and several others, in the past and currently, I believe the Olympian Wave 8 is the better option, but if price is a factor in the decision, or there is a lot of area to be heated, then the infrared LP heaters I mentioned will certainly work in the OP's situation. Wave heaters DO need to be covered when not in use to keep the platinum pad in good shape. Infrared and blue flame heaters have no platinum pad so they don't need to be covered.
Disclaimer: All safety measures (in the use of these un-vented LP heaters) by the installer and owner are assumed.