If you are concerned about the temperatures they should be OK at 6 weeks as long as they are out of the wind and have decent ventilation. I've had chicks younger than that go through nights with lower temperatures. The problem may be where they sleep. You never know how that will work out when you integrate.
If you are talking about how to integrate them it gets a lot more complicated. How much room you have in the coop, how much room in the run, the quality of that room, and when it is available are all important factors. By the quality of that room I mean do they have places they can hide from the older ones to break line of sight.
That is encouraging. If you have sufficient room you may be able to just merge them in with the adults. If you try it that way do it during the day when you can monitor and see how it goes. Sometimes it is that easy. I'll harp on it again, the more room you have the more likely it is to work. If you have a typical tight backyard set-up it's not that likely to be this easy.
The way I'd try this would be to put out extra feeding and watering stations so the older ones cannot bully them away from food and water and then turn the young ones loose. See what happens and base your actions on what you see. If it works out the chicks probably won't go into the coop at dark, you'll have to lock them inside. Wait until it is dark enough that the older ones can't beat them up overnight. Make sure the coop is dark, not lit up by a security camera or something like that through a window. Then be out there first thing the next morning to see how it is going. Do not leave them locked inside that coop with the adults when they are awake until you are comfortable they will be OK. My situation is different from yours but that's practically always two mornings for me. What I often find is the chicks sleep on the coop floor somewhere but after they wake up the chicks are safely up on the roosts while the adults are on the coop floor. My roosts are high enough that they are a safe place away from the adults. I have no idea how big your coop is, what it looks like, or how high your roosts are.
If this doesn't work out put the chicks in a predator-safe weather-safe area across wire form the adults for a while. Proceed from there.