No, they won't be funky as long as you have their respective probes in the right place. The one below the CHE (hanging just inside the tank or sitting on the lid below it are the common locations, I think) would not be seeing floor temps and the floor probe outside the tank would be reading the UTH itself and not be effected by the in tank ambient temperature.
A dimmer is ok for CHE (far better than none), but a thermostat is much safer... if there is a fluctuation in your room temperature up (say, 75 turns into 80 one day), it will still provide the same amount of power and what was 80 ambient is not 85 ambient. You see?
I do know that the less expensive thermostats are on/off types are not favored for CHE. Those bulbs can get very hot very fast with full power and may get pretty hot for short bursts. Not super likely to cause an accident if the bulb is in a dome on top of the screen (not inside the tank), but there is some risk of it heating part of the screen itself above the temp you want before the thermostat registers the change and turns back off. I'm not sure if it's enough to cause a burn since they cant lay on the ceiling, but something that would concern me personally. (vs the Herpstat 1, 2, or 4 which provides a percentage of power to get a desired temp AKA proportional)
If you do think about getting a thermostat for it, I'd highly suggest the Herpstat 2. Then you could control both your UTH and CHE in one unit and take advantage of the proportional power control to keep things safe for your noodle.
It would also be beneficial to put some sort of insulation like that pink insulation foam from the hardware store where you can. Even if only back side and the bottom will help . Especially if you have it on a table with air below that would be you room temp. Heat escapes through glass itself very easily. (One main reason people really like PVC/plastic enclosures on here)
The plastic lid cover would be a very snazzy option since you have access to tools/help. If I kept glass tanks, I would wish I could do that too.
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