They could have been cautious.
If the day heat really messing up with the ear thermo reading, you might have noticed more babies being sent to the hospital. The ear thermo are actually pretty realiable.

Im not going to be bothered asking more for your kids history but the doctor might have gotten enough to warrant such suspicion.

I noticed youve mentioned your kid seem kalm even in that heat. They might think baby is lethargic.

If the staffs really are bad, they would have just send you home despite the temperature.

All things considered, seems like you are mainly dissatisfied with the wait and the heat. Ill say that's good enough to complain. Hopefully they will do something about it besides putting patients in tents.

But ill say it again, nothing seems out of the ordinary in your kids management.