I am still confused as to why you say having the probe on the outside of the enclosure requires you to mess with the settings. If your probe is directly on the heat source then it shouldn't matter. That is the point of the tstat to maintain a steady temp. So for arguement sake lets say you have the probe directly attached to the heat mat OUTSIDE the tank, and you set it to 92 degrees, you have a slight temp variance on the inside of the tank a few degrees off depending on material. Once you get it dialed in to the correct temp it will maintain that set temp. IF the temp drops in the room it will bump the power being delivered to that heat mat to again reach the temp you set it to, which in turn keeps the inside of the enclosure the same temp as before.
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I too agree, tape inside the enclosure is a no no.