How about a folded towel inserted into the steamer insert of a rice cooker? If you put in just a small amount of water, it won't take much energy to boil it and then it will switch over to the warm mode. Of course, it's going to have to be either a small towel or a large rice cooker.

Another option would be to stick it into a coffee pot of a standard coffee-maker. The base would keep it warm but this would be a greater fire risk if all of the water evaporates.

Another option would be to soak the towel in hot water in your sink.