Well, you can do this with a TEC. You'd need a heatsink and fan for each side of the TEC and a DC power supply to drive the TEC (and fans). You could switch the DC supply on and off with your thermostat.

You have to figure out how large a TEC you need though. That's a relatively small space but the lights will dump heat into it and heat in infiltrate via the glass.

You probably need something on the order of 40 - 80 watts of cooling power. Probably a 50mm size TEC. Perhaps a 60mm x 60mm heat sink on the cold size with a 60mm 12VDC fan on it. Then on the hot side, a 60mm x 120mm heatsink with another 60mm 12VDC fan (or two). Some 5mm or so of neoprene to elevate the hot side slightly over the plastic enclosure top and insulate the top from the heat.

The longer hot side heat sink simply prevents the whole thing from falling through the 60mm square hole you'll have to cut. The hot side also has to get rid of both the heat you draw from the inside and the power you send to the TEC to do that work. Though you could just cut a 52mm square hole if you can remove the lid for installation where just the TEC itself is in the hole.

If you ran a CustomThermoelectric part like 19911-5M31-12CW at 12VDC you could probably pull 40 watts from the inside with the cold side at 10 degrees Celcius and the hot side at 40 degrees Celcius. I'm just spit balling here.

Seems like an interesting project.

I don't know that you need an AIO. They are notoriously low flow poor performers. I was thinking you might get away with air cooling on the hot side but that would probably be larger than you'd want to see.

You could insulate the tank obviously, though 2-1/2 inches is a bit much. But then you're killing part of the view. I do see a water loop on the hot side as being the best way to keep the noise down and the ability to remotely locate the radiator would help to keep a clean look to the whole package.

A 120 of a decent thickness would probably suffice. Using water cooling for the hot side would probably allow you to use a smaller Peltier as well.

You only want about 10 degC or slightly more on the cold side. You could probably then plan on a Peltier differential of 25 - 35 degC.

yes water cooling is far better but i doubt you'll need it in your case cos you're not shooting for a huge delta or massive amounts of heat load

You'll need to apply pressure to the the TEC so you'll need to bolt the hot and cold side heat sinks together

Have you seen my TEC Youtube channel ?
https://www.youtube.com/user/Ultrasonictwo

you'll have to excuse my ignorance but what is AIO?

yip

I think that would be just fine. A heatsink using convention on the cold side within the terrarium and an AIO on the hot side to absorb the heat moved and reject it quietly to the atmosphere.