Are you sure? He has been pampered inside a house with warm temps his whole life. Can I just place him outside all at once when it freezes at night or is that cruel?
Am I sure those temperatures won't hurt him, yes. Am I sure of anything else? No. I don't know enough of the other circumstances to feel like I understand what is going on, especially with integration.
Also, chickens generally don't like change. Moving him will be a change, there might be parts of that move he doesn't like. Chickens are also pretty adaptable, my brooder chicks usually get used to being in total darkness for the first time in about 15 minutes or less. They might complain for a while though. He may not like being in a strange place for longer than that, but he will adapt. Or he may love it out there, I really don't know. But will those temperatures hurt a healthy cockerel that age, not in the least.