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I've set the water temp at 81 it gets a bit warmer when the lights are on. Is this a good temp for a hatchling about 1
Inch in length?

It's a bit warm. You can drop the temp to around 78 degrees. When he gets to be around 4" long, you can drop it some more to 72 to 75 degrees.

Sorry, I just saw your other post about how he's a brand new foundling. Since he's lethargic and you're not sure yet that he's healthy, go ahead and leave the temp at 81 degrees. It will help stimulate his immune system.