Unfortunately, when you deal with living animals you have to also deal with dead animals. The chick was a month old, that eliminates a lot of things. The others all appear healthy, so did this chick last night. I don't think this had anything to do with heat or cold. Not diet either, the others are fine.
Did you inspect the chick to see if it had been injured? What I'd look for would be a cut, puncture, or gash as it had been pecked, bitten, or clawed. Many critters like to attack the head so look there but check the vent area and entire body.
I consider poisoning but in your case I think that is extremely unlikely. There aren't that many bugs or such that would kill it even if it ate the bug, it might get sick but not die that quickly. The other chicks are fine. I'll mention poison because you are looking at them and I'm not, you might think of something, but I don't think this is the problem.
I've found a couple of hens dead in the coop or run for no apparent reason. No previous suffering or signs. I think they had an accident, probably broke their neck banging into something, maybe trying to get away from an amorous rooster or away from a pecking order fight. Chicks can sometimes get pretty active when playing in the brooder.
My guess is that the chick had a birth defect, maybe a faulty heart or such and had a heart attack or stroke. There is no way to know anything is wrong with them until they just fall over dead.
If something happens to another chick get back to us, a pattern suggests something is wrong. But if it is just one time I consider it bad luck.