I'm going to be blunt. If all three chicks are the same breed and should be the same size, it is extremely likely that something is seriously wrong with that chick. If it could be a bantam and the others are not, then it could be a different story. There is a lot I don't know about your situation.
I've had a runt before. The same parents as other chicks but it was always small from shortly after hatch. By the time I processed it at 18 weeks (I was not going to let it breed) it was maybe 1/3 the size of the other roosters it hatched with. Some of its internal organs were very small, even considering proportions relative to its small body size. It behaved normally though, not like your chick.
That constant peeping means it is in some type of distress. If the others are not cold, I would not think cold is your problem. It could be something physical, like it is in pain or maybe hungry or thirsty. There could be an internal restriction in its digestive sytem. It may be something emotional, like it does not realize there are other chicks in there. Maybe it is blind? That might explain a few things. Maybe it is mentally off? I've had some really mentally challenged hens before. It could be about anything.
I don't know your reasons for having chickens. That is your business. I'm not telling you that you need to put it out if its misery. It may outgrow whatever is distressing it. I sure can't tell you what you need to do. But I will suggest that if your goals include breeding chickens, that one should not be allowed to breed if it makes it.
Good luck.
