I used a springy hair clip - the kind you clip onto a twisted ponytail, and tied a string from a feed sack through the eye of the thermometer. Works like a charm to clip to the tail. You can use them multiple times.
You ease it in there, slowly, kind of twisting back and forth, and then it doesn't hurt the horse. It only has to go in far enough to make contact with the walls of the anus and you don't want it to be in manure.
OK to use some lubricant like mineral oil but it will make it harder to read.