My lot, BR's went out to their coop 2 weeks ago at 3 weeks old, No light or heat. Had to put a fan on them during that heat wave, fed cold yogurt in the heat of the day, and changed their water every 1-2 hours, They are now 5 weeks and doing great! Had no problems with the move and my temps, after the heat wave, dropped to 75 avg days and 55 avg nights. I just close the windows, a bit before it starts cooling down for the night, since we don't have the shakes and trim on yet, till the run is done, it has plenty of ventilation!!!
What breed do you have? How are they doing feathering out?
Mine are large fowl, dual purpose and are cold hardy. Only had heat on them for about a week and they never did like the 90-95 degree suggested. I would be leary to put a heat lamp in the coop.
At 4.5 weeks old, that's older than when my lot when out, I live in way northern New Hampshire, at the top of a mountain.
It's up to you, but it is summer, so not quite the same as brooding during the spring or colder months. As long as you can keep them dry, the rain should not be an issue.
Mine are still in their coop, as the run isn't finished, but we have had ton a rain here too, lately...so far, all is good here!!!
Best of luck