Boiling point of propane is -42 Degrees C at atmospheric pressure. It only stays liquid because it's under 7 or 8 BAR of pressure. Drop the pressure to 1 bar in the vapouriser and it boils pretty quickly.
However, it still absorbs heat energy whil boiling due to its' latent heat of vapourisation so if the vapouriser were not heated it would steadily cool until it was no longer able to boil the liquid.
It needs about a kilowatt of heat energy to boil enough LPG to run the engine during motorway cruising.
Next time you're at a market (or wherever), especially this time of year, have a look round the back of the burger van and you'll see a layer of frost on the propane cylinder if they're using gas at a reasonable rate.
The gas in the cylinder is boiling off as they draw vapour out of the top and it has to cool down to absorb heat. This causes water vapour to condense and eventually freeze on the cylinder.
Butane gas boils at a much higher temperature (only just below freezing point IIRC) which makes it ideal for camping in the summer but no use outside in winter because it doesn't boil off in the cylinder. It's often mixed with Propane to improve its' performance. Or the cylinder is placed on a burner of the stove for a while to liven it up.
Kevin