the thermostat probe should NOT be inside the enclosure. even if you think you've taken every precaution of preventing variables that can change the reading, the risk you're taking is just not worth the consequences.
the thermostat probe sandwiched between the bottom of the enclosure and the UTH is not just about accuracy but preventing any type of misreading, fluctuation or variable that can change the reading, and keeping the temp as steady as possible. you can use aluminum tape to adhere the probe to the underside of the UTH (not between the UTH and enclosure) if you don't want to sandwich it.
the risk just isn't worth it. this forum has seen far too many unhappy endings with this same scenario.