Consider what is actually happening. There are sensors in the head that report to the main control through that white cable. The sensor could have a problem, a clip on the way to the white cable may have a bad connection, or other sensors put to use the orange light since the original machines (like the carriage fan working) could be telling you there is a problem, or there could be something overheating the head and not the ambient air that was the problem. If you turn the machine on and the orange light comes on no matter the temperature of the room then it is not the air temperature in the room, (though that is a first thing to check.)
If you check what you can check and take photos of what you have checked, what the screen is saying then reply to the email they sent you (rather than sending another one) with that or any other information they send you.
The good thing about a Glowforge is that you don’t have to be a master of mechanics, electronics, and programming spending all your time doing those things. The bad part of the same fact is that much of it is a black box that you can’t do them. There are few user fixable parts so if you cannot replace a part (like the carriage assembly) the whole machine needs to go back to the factory.
Therefore the main thing you can do is to make really sure that is the case, rather than presuming that is the case.