the probes for the t-stat go outside the tub. i tape mine underneath the UTH and some put it between the tub and UTH. the thermometer probe should go underneath ur substrate right on the tub underneath ur snakes hide.
and also, when using a uth that doesnt heat up the cool side to 80 or higher ill just put a red light on a low setting on the cool side to keep it around 80 during winter