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[MrBredli]

You don't need a heat gradient. If they want to warm up they will bask under the lights. If they want to cool down they'll move away from the light or into the water.

I don't think they would be able to grip the chain, but you would need to use a dome so that they can't fall directly onto the light, and the underpart of the dome should be covered with wire mesh so that they can't jump up into the light (and burn themselves).

How many do you intend to keep in this cage?