You might consider placing an electrical, far infrared radiant carbon thin film under your vinyl floor or carpet. It is 0.017" thick, in widths of 30, 40, 50, 60, 80 and 100 cm. Most common use is under wood floors. Koreans and Europeans use in floors, walls and ceilings. Just remember where it is, so a fasterner or drill doesn't go through it. :E
My plan is to intall it on the part of the wall surfaces and floor under the dinnette. Even though it runs on 120VAC, I figure on using it while I charge my batteries once they are out of the bulk phase of charging. Uses 200 W per meter squared film. Your inverter and battery bank could handle this.
Typical boiler based radiant heat systems inputs use:
105 - 115 F for water temp for wood floors (too high heat causes shrinkage due to drying)
85 - 105 F for tile / contrete floors (conducts heat well)
115 - 135 F for carpet (pad /carpet combination more an insulator)
Goal is to keep finished floor temp < 82 - 85 F. Suggests having thermostats that have temperature sensors that are located on the thin film to limit max temperature of floor as well as one for room temperature. Less regulated systems use lower W/m^2 films. Third generation films have a positive temperature coefficient which use less current when warm and less likely to overheat.
Websites to get an idea:
RexVa - XiCA carbon infared heating filmRexVA - Positive temperature coefficient heating filmKorea Heating EUFenixLots of Youtube videos showing installation
Carbon Heating FilmKey elements of the installation of infrared heating filmInfrared Underfloor Heating System - InstallationA little for surfing the web will find current suppliers in the US and eBay. Simple systems can even be found at Home Depot (Quiet warmth)