I think it would be a lot safer to just put a fan blowing air over the bottles.
As propane evaporates from the liquid in the bottle the latent heat of vaporization must be replaced. In ordinary conditions, enough heat will transfer into the tank to make up this latent heat and even though the bottle will drop in temperature, gas will still come out. In very cold conditions, you will not get enough heat transfer.
While a heater of some sort will work, the real problem is finding one rated for this service. While there are a lot of heaters which are probably safe for this application, getting one the manufacturer is willing to recommend and test for this is going to be difficult. The market is small, but the liability is large.
A fan will increase the heat transfer rate from the ambient air to the propane bottle without ever contacting the bottle. It is an inexpensive way to do a lot of good.