I don't see any reason why it wouldn't work, though I'm certainly not an expert. One thing I do understand pretty well, though is energy balance. You are basically suggesting that you are going to take a machine whose job it is to expel heat from the system, and place inside of it a device whose job it is to add heat to a system. I, personally, would want to monitor the amount (cost, really) of electricity this setup would use. You're paying to bring the electricity in to heat up the water and the cheese area, and then paying to remove that same heat from the fridge. It might work great--it really just depends on the difference in the set temperatures for the cheese area vs the rest of the fridge area, and how well you can insulate the one from the other. If you can do it well, it won't cost much, if you can't, it will cost a lot and might reduce the life of your fridge.
I use a kill a watt meter to measure how much it costs me to maintain my cheese cave at the right temperature. Right now, it's about $6.50/month-tolerable.
If you do it, let us know how it turns out.