You have two issues. One is integration. I don’t know enough about your specific set-up but it’s generally a good idea to house them next to each other for a week or more before you let them mingle. Having a lot of room can help too. I regularly integrate 5 week olds but my brooder is in the coop so they grow up with the flock. And I have a lot of room. I keep separate feeding and watering stations so they don’t have to compete with the bigs to eat and drink. I have a mature rooster which I think helps. There is a lot of good information (and some bad) on this forum about integration. If you can give us some specifics of your set-up like size of coop and run, number of the different aged chickens, whether they free range or how they are confined, we may be able to offer some specific suggestions. A few photos could really help.
The other issue is are they ready for those temperatures without heat? Probably not, especially at night. Most chicks fully feather out at 4 to 5 weeks and can handle really cold temperatures. But I suspect yours have been kept at tropical or subtropical conditions in your house and are making a mess with dust, noise may be an issue, or possibly smell. You are probably ready to get them outside. Going from the tropics to near freezing can be a challenge, I don’t like doing it even if I’m dressed for it.
My 3’ x 6’ brooder is in the coop. My chicks go straight there from the incubator or the post office, even when it is below freezing outside. If you can set up a safe place for them where the older chickens cannot get to them, you can keep from starting a fire with your heat lamp, and you can keep one area warm but let other parts of the brooder cool off, yours could have been outside for four weeks. They can certainly go out now.
I use heat lamps held firmly in place with wire but there are other methods to provide heat. A real popular way right now is the heating pad cave which you can probably find with a search but others use different methods. What you are trying to accomplish is to keep one area warm enough no matter how cold it gets and one area cool enough no matter how warm it gets. With varying temperatures outside that can be a bit of a challenge but they are extremely good at self-regulating, even straight out of the incubator. Yours would have no problems self-regulating.
I’ve had chicks raised in my brooder go through nights without heat at less than six weeks of age with temperatures in the mid 20’s Fahrenheit. But mine were raised in a brooder that might have ice on the far end when it really got cold in the morning. They were acclimated, had good wind protection, and had good ventilation. If you can provide the right conditions they can go outside now.