If a camera in a waterproof housing heat up to a degree where it shut down, then i think you will have to submerging that camera and housing in water so cold it will be no pleasure to swim in, and then there might also be a tendency to dew inside the case.
And i find it hard to see a feasible way to transfer heat from the inside of the camera and all the way out to the plastic casing, and then dissipate that heat there as plastic after all have a low thermal conductivity.
There are a range of ways to get heat off a hot thing to dissipate it elsewhere, but to have the best chance of success you will need to tap in directly on the heat source like a heat-sink on a CPU in a computer.
In a computer case a good flow of air inside the came will also improve the performance of the heat-sink on the CPU as it is after all that air the heat-sink dissipate the heat into, and so you got to get that hot air out or you will see a build up of temperatures inside the case.
Years ago a Danish company named Danamics came up with a revolutionary new CPU cooler, that was sort of like a heatpipe cooler, but inside was liquid metal that was circulated by a magnet.
Only problem was on the other end where the trapped heat had to be dissipated into air, it was just like any other CPU cooler and so its performance was similar to regular heat-pipe coolers costing 1/4 of that fancy cooler.
https://www.engadget.com/2008/12/05/danamics-liquid-metal-cpu-cooler-found-to-be-impractical-ineffe/