It is not the "coolness" that stimulates the change in hormones that stops the broody state. Actually, it is just the removal of any nice nesting place and a wire cage can do that--or bare floor--or any place that is not a "nest".

Actually you do not "cool" the hen, as her temperature has already cooled several degrees when she becomes broody. Normal chicken temp 103 (egg, when laid, 104)--hatching temperature is 99.5 to 100. It is the total removal of the nesting stimulous that will change hormone level back (and temperature)to normal. And it will return without any help, but it is hard on the hen, who is lacking proper nutrition, even if she eats a little, and exercise, while she is just sitting. CJR (Even if we do call it "cooling off"!)