I have made something similar to what you are talking about but make sure you have enough power that you don't blow your circuits. Also if you have to much power it will melt your bowls.
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Wouldn't you be able to have them start around 5am and off around dusk? only problem that there might be is the light not being on able to thaw the ice in a hour or so.Yes I'm going to get a couple more timers to offset the amount of heaters on and the bowls will be on a thick floor tile slate