Yes, do not lock them in a new coop. Too hot, but rather give them the choice of in or out. At nine weeks they should be strong enough to take a bit of heat with good air flow, water and shade options.
As long as the coop and run are attached, mine have always made the set up imprinted on them. I would never lock my birds in a coop this time of year, except at night, and only if I was sure I would be able to open it in the morning. This time of year, I keep the chicken door open all the time. It is in a secure run.
One thing to do is check your shade in the run through out the day. My current run has very nice shade in the morning to mid afternoon, but by late afternoon, the hottest part of the day, the shade needs help. I rearrange some pallets to give some shade options for that time of day.
If you have kept them in the house for 9 weeks, without outside time, I would add them late in the afternoon, make sure they get in the coop for night, and monitor them closely during the next day. Probably over cautious, but prudent.
Mrs K