When I think of quantum cooling I think of laser cooling. Which is cool. But that's an article that is meant only for devout quantum physicists. I say if something even remotely close to what they want to do is actually shown in a real experiment then I'll first eat my own shoe and second I'll stop making fun of quantum mechanics. I wouldn't count on it though.
P.S. the math seems right though. So it's not silly in that sense.