Let's have some fun with propane! I may come off as a Hank Hill but here goes. Let's start with a video of some very cold propane. This will give you a visual demonstration of the effect of heat on propane.
Next here is some geek stuff on the science of the Vaporization of propane.
Your LP-Gas cylinder or tank is filled with liquid propane, while your equipment burns vapor. How does this all work?
LP-Gas (propane, butane, LPG) is transported and stored as a liquid under pressure. In order for your equipment to be able to use the propane1 in your storage vessel (cylinder or tank) it must undergo a phase change (vaporization) from liquid to vapor within the cylinder, before being combusted by your consuming equipment (BBQ, radiant heater, boiler, process burner, etc.). The rate of natural vaporization in your tank is essentially a function of two factors: 1) ambient temperature; 2) tank size and fill level ("wetted" tank surface area). Each piece of propane consuming equipment has its own requirements as to the amount of vapor that it needs to run properly.
Vaporization Requires Energy (Heat)
Propane, like water, is a "compound" with its own set of chemical properties. At atmospheric pressure, water, a substance that we are all very familiar with, boils -- that is to say goes through a phase change from liquid to vapor -- at 212 degrees Fahrenheit (100 degrees Celsius). Propane, on the other hand, as a result of its particular set of chemical properties, boils at -44 degrees Fahrenheit (-42 degrees Celsius). Therefore, as long as your propane tank is stored in an area that is at least -44 degrees F. (at sea level), the propane in your tank is undergoing phase change, and the pressure will be great enough to give off at least some vapor pressure.
Now, to complicate things, the phase change of propane, just like that of water, involves the transfer of energy. You cannot boil water without an outside source of heat from, say, the burner on your stove. Further, the more energy applied (the hotter the burner), the faster your water is boiled, and the faster it is expelled into the atmosphere as vapor. Similarly, with propane, a warmer ambient temperature (above -44 F) results in a higher rate of vaporization and greater vapor pressure, allowing you to draw more vapor off the top of your cylinder. Based upon this discussion, it should be fairly evident that ambient temperature has a direct effect on the ability to run your equipment. If your equipment is asking for more vapor pressure than can be provided naturally by ambient heat, it may shut down (or merely provide less heat than you require).
Properties of Hydrocarbons
Tank Size and Fill Level--the "Wetted" Surface of the Tank
Now that we have briefly discussed the direct effect of temperature (energy) on vaporization, lets now turn to the effects of tank size and fill level. Let's continue with the water analogy. Say you have two pots of boiling water, one 2 quarts and another 2 gallons. The 2 gallon pot is going to give off more vapor than the 2 quart pot, so long as the heat being applied is held constant. The same is true for propane--the larger and fuller a tank is (the more "wetted" surface it has), the more heat transfer surface area, and the more vapor it is going to give off.
These two factors, heat and heat transfer area (tank size and fill level), directly affect the natural vaporization rate of the propane in your tank. It should be fairly easy to see that if you are relying purely on natural vaporization in order to run your equipment, you are at the mercy of these two factors.
If you've ever seen a layer of frost form on your propane tank or bottle, you have seen first hand the limits of natural vaporization. Seeing frost on your tank means that the rate of heat being transferred into the tank to the liquid propane is less than the energy being used to actually convert the liquid to vapor, which results in a pressure reduction thus creating a refrigeration effect. This refrigeration effect continually reduces the rate of vaporization by forming an insulating frost layer on the tank, further causing a loss of vapor pressure. This can have a devastating effect on your ability to run your equipment.
If you notice that your propane consuming equipment isn't giving off quite as much heat as it should, you should also suspect insufficient natural vaporization--quite simply, the pressure of the vapor reaching the burner has decreased below that which is required for optimal heat output.
If the rate of natural vaporization is a function of two factors--ambient temperature and wetted tank surface--as discussed above, the question becomes: how do you increase your rate of natural vaporization. Unfortunately, you can't control the outside temperature, so what does that leave you with? Wetted surface area. Simply put, in order to increase your wetted surface area you can either 1) increase your tank size or ensure that your tank is always "full."
Since your tank is not always full you can expect performance to fall off so leave you tank in the sun or you can dunk it in the river.