The only heat required in a propane fuel system is in the regulator/convertor. Liquid propane, like LIQUID gasoline will not burn. Propane at normal temperatures is a gas. I cannot remember the temperature that propane becomes a liquid, but it is pretty cold (like -50 or so???)
Anyway, when propane as a liquid becomes a gas, it evaporates which has a cooling effect, hence the need for heat in the convertor/regulator to keep it from icing up. The propane in the tank will not evaporate fast enough on its own to run an engine under full power, so hot water basically boils the liquid propane, so the engine will have enough vapor to run on. Once the propane is a vapor, it has to be pressurized (250-300 psi) or supercooled to become a liquid again. That is where propane has an atvantage over gas. In normal operation conditions, propane is a vapor and will stay suspended in the intake manifold to be burned by the engine. It is a much cleaner fuel to handle and burn because it does not have all the additives and contaminants that gasoline has. It does NOT have the BTU energy that gasoline has, so it will not produce as much power.
I remember some guy around Wichita KS about 25 years ago that built a heat exchanger that vaporized gasoline which he then ran in a propane carburetor. They were interviewing him on TV and the reporter asked him if his pickup (a 66 Chevy pickup) showed any difference in power or economy with this invention. He said he was getting 60 mpg pretty regular. The reporter asked about power again, and the guy got this sly grin on his face. He jumped in the quietly idling pickup and smoked BOTH tires (posi) all the way down the block and most of the way down the next block before he backed out of it. The smoke cleared just enought for the reporter to surmise that power was not a problem and the story ended.