Room..yes..heat source no. My coop is a ways from my house with no power source. I’m in Kentucky and it’s usually late April, early May before it’s warm enough for 8 week old chicks.
How far, in feet? Any chance of using a heavy duty outdoor rated extension cord for a few weeks?
They won't need heat after about 4-5 weeks.
I like to brood and integrate when chicks are young,
much easier than when they are older, tho it takes some prep of a good space.
This is how I do it...and there's some links near the bottom of simpler setups:
https://www.backyardchickens.com/articles/integrating-new-birds-at-4-weeks-old.72603/
I still follow the.......
Integration Basics:
It's all about territory and resources(space/food/water).
Existing birds will almost always attack new ones to defend their resources.
Understanding chicken behaviors is essential to integrating new birds into your flock.
Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact.
In adjacent runs, spread scratch grains along the dividing mesh, best if mesh is just big enough for birds to stick their head thru, so they get used to eating together.
The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.
Places for the new birds to hide 'out of line of sight'(but not a dead end trap) and/or up and away from any bully birds. Roosts, pallets or boards leaned up against walls or up on concrete blocks, old chairs tables, branches, logs, stumps out in the run can
really help. Lots of diversion and places to 'hide' instead of bare wide open run.