LP (propane) heat is a great source of heat for carpet cleaning, and very safe. It is very clean burning, so much so that here in several Ohio counties, where vehicles emissions testing is required, if you have a vehicle that runs on LP, you are exempt from this testing procedure when you re-license your vehicle.
We happen to produce the only patented flow fired heater with an electronic ignition, as Larry asked about in his post above, that will NOT ever blow out on windy days. The best part of the electronic ignition is all you need to do with our heater is flip a switch to turn it on. When you are finished cleaning just turn it off. No pilot to ever mess with - a great feature if you have employees.
Our patented afterburner circuit then proceeds to squeeze more heat out of every btu than other flow-fired LP heaters because it will continue to heat the water even when you release the wand trigger, until the heat setting you dialed in on the temperature dial is met, or the patented timer ends it's cycle. Then it will come back on when the heat starts to drop to prevent heat spikes.
Our heater will also run when using a low-flow tool such as an upholstery tool, something a lot of these flow fired heaters won't do.
BTW, I have been cleaning using propane for 22 years exclusively, and have never found it a hassle to fill the LP tank. There are several places in town that fill van mount tanks. Look at your LP gauge every day before you leave, or better yet, check it toward the end of the day, and get it topped of before you return for the day.