if you have ever seen a snake wrapped up in tape you would never suggest tape inside an enclosure. im guessing you havent. i have and its not a pretty site.
if you want to put the probe inside the tub you can drill small holes in the tub over the area where the heat source is and use a zip tie or a twist tie. use tape on the under side of the enclosure to keep spilled water or urine from leaking out of the holes.