Liquid cooling is really the only way to go if these are going to be waterproof. But you will need a heat sink which protrudes through the rubber layer. I suppose the simplest way to build what you want, would be to coat the whole thing in a waterproof layer of shock absorbing rubber, then run either heat pipes or water pipes through the case and the rubber, terminating on a large copper plate, ideally on the top of the screen. Maybe another one underneath. You'll need fins or something on the bottom one to allow air to circulate.
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