I'll shed a little light on the subject, for those who are unaware of the dynamics of propane...
The reason the propane cools off is due to decompression (adiabatic cooling). It is entirely possible to get the propane cylinder so cold that it will completely stop putting off vapors. This is where the water bath comes in. It is not possible to overheat the propane cylinder unless you're using water that's over 100 degrees, as this is how hot a propane cylinder might get from ambient outdoor temperatures.
The question remains, does the cylinder have enough output to run the L5 (or is it L10?) heater? Easy enough to answer, if it has the output to do it for more than 10-20 seconds then it has the output to do it indefinitely, it just comes down to a heat/cold balance within the liquid propane itself.
A larger tank has a larger "heat bank" to draw from before it goes below it's boiling point than a smaller tank would. You can easily get a 20lb tank too cold to off-gas, done it plenty of times. Same reason that a propane heater on a porch will have poor performance if the tanks are left in the shade in January. You can put a 20lb tank in a tub of warm water to help as well.
Finally, 20 years of hazmat experience pays off!