When i mean thermostat, i'm talking about a little machine with a plug that disconnects the lamp when the set temperature is reached, i think you ment to say thermometers? If you've a thermostat, get a 100w and a dimmer so you can set it to arround 60w/70w, if you don't buy the one i talked about which do both in one machine if you'd like.
Anyway, you'll need a thermostat, a CHE running full blast day and night will certainly cook your frog...
For the hygrometers, that's normal, they're all bad even the expensive ones... Believe me, i tried, most of them have the same sensor... Same to me, do the salt test (slimy gue of salt and water inside a sealed bag with the hygrometer) that should read 75percent, if it reads 79 write with a pencil +4 for example in the hygrometer, so you know.
Yes, the tank should be half the size, at least three sides covered, or a black tupperware. Is he an albino? If he is, LED light with no more than 100lm and something yellow/reddish, around 1W. Don't even think about UVB/UVA.
Mine is in a tupperware inside the tank...
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For the links, i've sent you a PM, but since you're in the US, the items will not be the same as in france, but you'll find the same ones i guess, or at least a lot look a like.