I'd keep it on the outside of the tub since the snake will most likely be a nosy stinker and somehow move that tape.

If you can wrap the probe with a multiple-folded paper towel and tape it to the flexwatt, that should make a good buffer and the air temp won't be able to affect it. Set the tstat to about 95 or so when doing this and see what the temps in the tub are doing in 30 minutes to an hour after everything has settled.