1) Its a closed system. The starting temperature of the water wont make any difference, other than it will take somewhat longer to cool down the hotter it is to start with.
2) Also, your going to be turning the compressor on and off with an external thermostat. It wont be any different from starting it up the first time you plug one in, before it cools down.
3) This is no different from how any chiller or any refer works. Its also just like your home refrigerator, which keeps food above freezing on the warm side. My fridge can be turned up to around 50 F with its internal thermostat.
The fact your not trying to cool the water down to freezing will actually make it work less hard because of the smaller temp differential.
Ok, even though Im right, and you guys are e all WRONG, I'll stop arguing. Im obviously in the minority.
Sorry to let you down Atomizer. I gave it my best shot