Ever wonder why the oceans don't freeze from the bottom up? After all, it's a lot colder at the bottom of the ocean than at the surface. It's because water is one of the very few substances that expand when they freeze.
So you're assuming that the warmer water at the bottom of the tank will keep the surface from freezing, because as the water cools it will descend from the top to the bottom. That works until you get down to around 39 degrees F, when water reaches its maximum density. Once water gets colder than 39F, it starts to expand, so now the colder water rises to the top of the tank, where it just gets colder.
So, no, I don't think your idea will work. But give it a shot and let us know how it turns out.