Welcome to BYC
@HenPecked65!
At this point, not sure locking them up would do the trick and the heat is definitely a concern.
How big is your coop, in feet by feet?
Do you have 14 feet of roost length that is easy to get up and down from?
Do you have windows for light(and ventilation) in the coop?
Pics of your coop would help.
What I would do is put a light in the coop just before dusk,
one of those cheap battery operated puck lights works great for this.
You don't want it to be
really bright, so if it's an LED cover it a bit to dim the brightness.
I would also 'disturb' the place they normally gather in the run,
put a couple buckets or something that prevents them from lying there.
Might take a few nights to get them to go in as you've been carting them in for long time.