Depending on where your coop is located, you can run an extension cord to the coop, which is what I do. Although for many people that's impossible.
I don't know what kind of set up you have for your keets now, but here are some inexpensive suggestions for keeping keets and chicks separate, and brood them up in the house or garage (whatever).
PeepsCA makes "mini-brooders" out of large Sterilite bins - and now I do too. It's cheap, quick and very functional, AND it keeps a lot of the dust down. Find the largest clear bin you can and cut out a big square from the top cover, and cover the hole with hardware cloth. I put electrical wire around the perimeter of the hardware cloth so it doesn't snag my clothing or poke into my hands (I hate that stuff). Secure the cloth to the top of the bin by drilling holes into the top. Then use zip ties to attach the cloth to the top. Hang a heat lamp over it to the right temperature - raising it each week to lower the temp. Does that make sense?
I use these bins for my keets and chicks and it's good for about two weeks depending on how many keets/chicks you put in there. It might buy you some time with your chicks until the keets move outside. It will enable you to keep the keets and chicks separate. Keets larger than chicks will trample your chicks, so you really need to keep them separate.
You can also keep chicks (not keets) in a kiddie pool for a couple of weeks. I've done that too, but the dust from the chicks, feed and bedding is something I don't want to deal with twice.

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Big thanks to PeepsCA for all her info on this forum. Just about everything I've learned, I've learned from her. Well - actually, EVERYTHING I've learned has come from her. I read, read, read...
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