Mine will be 7 weeks, and I will put them out this Sunday. It's been a bit of a stretch, this weather hasn't wanted to meet me halfway. One thing I've done is raise the lights, and let the temperature in the garage get cooler at night. They are pretty well feathered, but the night temperatures are very cold. I think the garage temp under the lights gets down to around 50-55, and a few still huddle under the warmest spot. At 7 weeks, I aim to keep the temp 60-65, except nights. But I've only been doing that this last week and a half, knowing that they should be ready for some lower temps, just not as low as we've been getting.
How far is it from the coop to the house? If your chicks are almost old enough, and the house close enough, could you run a cord through the window, if you don't have outdoor outlets (use outdoor extension cord), and run the wire *over* to the coop? It will just be a few days or a handful of weeks at the most, though electricity to the coop sounds very, very nice.
I am getting anxious, and I am laying a fresh layer of shavings twice a day (about half still insist on bedding on the floor instead of the perches), and I need to buy another bale AGAIN! Their box is way, way overcrowded and I never expected them to still be inside the first week of May!