Sounds like a short then, so this is even when the craft is not armed? Just when they get power? That makes me strongly think it s a slow short, meaning there is resistance (otherwise it would have melted everything in less than a second).The motors are not connected. With battery connected and switch on, after a few seconds the Esc's are almost too hot to handle.
I checked out my Esc's last night and found 3 to get so hot it would burn you. Didn't see any bad connections or loose solder. There was discoloration on bottoms of the 3 escs. Is there anyone who can repair these? It's probably cheaper to just replace them.
Did you get it from Horizon Hobby? Have you spoken to them? Going from one hot ESC to three sounds more like a symptom. You need to determine the actual, underlying cause, I doubt that replacing ESCs (at $33 a pop) will cure anything.