When you use propane you use the gaseous propane floating on top of the liquid propane. This lowers the pressure of the propane gas. When the pressure of the propane gas lowers the liquid propane will vaporize the liquid propane. It takes energy to vaporize any liquid so the liquid cools. The cold liquid cools it's container. The air heats the container which heats the liquid propane.
If the liquid vaporizes faster it gets colder quicker. That is if it is colder outside you use more propane and everything gets colder quicker as the inside heats. As it gets colder outside it takes more heat energy to warm and vaporize the liquid propane so the liquid propane gets colder quicker.
The colder the bottle and liquid propane the quicker it will turn water vapor in the air into liquid water. The tank gets wet. The colder the tank gets below 32F (even if the air is still above freezing) the faster it freezes liquid water into ice. Ice insulates the bottle making it harder to turn liquid propane into gasnwhich you can use.
So, at some low temperature and some high use of propane you start to get less and less propane until you get none and you have no more heat.
Thus, the heat blanket then becomes useful under low temperatue, high humidity conditions.