So you you mean a completely sealed capsule/module that contains a miner that produces heat? And then you dunk it in?
Yes - drop it to the bottom, plug in power and ethernet, heat the hot tub and mine coins!
It would be nice if it could be WiFi too, but WiFi won't penetrate water worth a damn. So, Ethernet is the only choice.
Air is a very good insulator.
The air in the case will not effectively conduct the heat from the heatsinks to the outside of the case, because as D&T noted it has properties that cause insulation and not conduction. It would simply overheat and shut down.