I've thought about that also. There are also these things called plant heating mats that are waterproof. They are used for starting seeds but they might be useful as a waterproof heat source for under the tent.

I have used the heating cables for my palms when they were first planted...these cables are the same plumbers heat tapes that you plug in and it keeps the temps from freezing...this might help for some of your tropicals for a temperary fix...you can buy these in the big box stores. They come in 6 9 12 feet lenghts. I would wrap them around the heart of the palms and then tuck them in with Burlap..

Take care everyone,,,

Stat Warm...

Laura in VB

Maybe this can help out someone ...

I use soil warming coils on my citrus and my banana with good results but I don't really push it. I am in Massachusetts and I mostly use them to keep the trees safe during the cool nights of spring and fall but I bring them inside for the winter. The coils are a pain to get evenly distruted in the soil (the wires can't touch) but I came up with a method that worked well. If you are interested, let me know and I will illustrate it. There are also planters already rigged with heat called Thermoplanters but they only come in one size and they are pricey. I use the seed starting mats for really small plants but I don't think they're enough for a potted tree.

One thing to be careful of is the ratio of light to soil temperature. If you are keeping the soil warm but you are not giving enough light, you can get leaf drop.