Most chicks fully feather out at 4 to 5 weeks of age. He does not stay under the heat lamp because he is uncomfortable in that heat. With his down coat, he is too warm. You can turn the heat lamp off.
You don't say what the weather will be like this winter where you live. When I was growing up, we had chickens that would roost in trees in the winter. It was a tree well protected from the wind, but the air temperature would sometimes get below 0* F. He may not freeze to death by himself this winter even if he is on his own if you provide him a place to sleep out of the wind and weather.
I don't know what you mean by your hens won't accept him. Do they peck at him to teach him his place in the pecking order or do they try to kill him? That is two different things. Broody hens will wean their chicks anywhere from 4 weeks old to much older. She has already taken care of the integration issues, but not the pecking order issues. The other hens can be pretty mean to those chicks to teach them their place in the pecking order. The two places I notice it the most is on the roost as they are getting settled at night and at the feeder.
He is a little young to integrate but probably not too young to start. I don't know your set-up. If you have plenty of space, you can let him roam with the flock during the day. He probably will not mingle with them that much, though as a lone chick he might. I have not done it with a single chick. Set up an extra feeding and watering place or two so the others don't keep him away from the food and water. If yours are like mine, they will wipe out the feed you set up for him before they touch their own, even if it is the same feed, but he will get some. Provide him a separate place to sleep. Keep him in there a few nights so he gets used to it being home to him. Again, I don't know what will happen to a single chick. He may try to sleep with the others instead of going to his lonely bachelor pad. Eventually I would expect him to move into the coop with the others. How soon, I don't know.
This will probably not work if you keep them locked in a run all the time so he does not have room to get away, but if you have room, I think it has a pretty good shot at working.
Good luck!