I think you need a hint

While some of the guesses were quite entertaining, I think you all need another hint... One person did get quite close, though!

Here's one of those green things in use.
Looks like some heating device to keep the tiger's water bowl from freezing.
That's Jasmine, a "tabby tiger." It's a recessive genetic form in the same way the white tigers are due to a recessive gene. Jasmine is one of two tabbies we have, with her brother, Aasan the other.

I actually find that coloration more attractive than the white tiger, but it's never reached the "we much breed for it!" status white tigers have.
Those aren't actually self-watering, but are just heated. We still have to haul water in buckets from the nearest water spigot to the waterers, but don't (generally) have to break ice. In deep freezes, a thin layer will form on the top, but we can break it by hand easily enough it's no problem for the tigers to get through.

Those are also very simple to build, and consist only of a PVC pipe, stainless bucket, and pipe heater. If you want to look at one, they will be at my place until Sunday; feel free to stop by. I'm going to fill them tonight, in fact, and put them outside to check them out.
It seems like setting it up to keep it full shouldn't be that hard, although maybe not worth the trouble. Besides, gives you an excuse to spend more time with the cats. ;)
so close!
Water dish was my first guess, you know what fooled me? The height of it. It seemed too deep for water, but then I didn't realize you'd be nice and raise the water up to tiger height (so the inside pan might be much more shallow than the whole tube). So I had to go with the bambi-bits-chafing dish...
Re: so close!
Yeah, the height threw me off too. A heater element from a broken coffee maker would only need an inch of space, and even a 60 watt light bulb would need 6 inches at most. I couldn't imagine what kind of animal would need a water dish a foot and a half to two feet deep just to be able to drink.