I'm more concerned about the black mark on your chameleon's face since it's growing. I would get it to a vet. It could be a fungus.
In the meantime I would advise you to PM ferritinmyshoes and ask her to help. She's a vet.
OK, here are my thoughts about all this. I agree that the black area needs a vet's attention. It looks more like some sort of spreading infection than a burn to me...notice that it's not on the top of the head or casque but in folds of the neck and lower on the face?
About the cham's light color: let me try to re-state or clarify this for the OP. A cham that is very overheated can turn a pale color (and yes, it is a vague reflexive attempt to reflect heat, as light colors don't absorb heat as well as dark colors do). But if its that significantly overheated the cham would also probably be gaping (sitting with its mouth wide open) and attempting to get away from the heat source (hiding low in the cage). A cham that is so extremely stressed its in shock can also turn an odd blanched out color, but this color will show over the entire body and unlike any other coloration or pattern you'll see. For example, I've watched a choking melleri (normally bright leaf green with yellow bands and black spotting) turn a sickly yellow with orange bands. IMHO I don't think this is what's going on here. A cham that is dying has lost control of its color change process and it can show odd patches of very dark or very light color on different areas of the body such as the back half, only the head, the entire tail, or the body above the lateral line area.
As for "sleeping in your hand" this is not normal. Your cham could simply not want to go back into a confined space...once they know they can roam a larger area a cage isn't as attractive. A cage that is too low, too hot, too small can stress them out. Or your cham could be so stressed out by handling it closes its eyes and lays quiet in your hand, or its exhausted by something in its environment. It may well be sick (possibly the infection process on its head is painful or spreading internally).
IMHO, take this cham to a vet so the black patch can be sampled, biopsied, and inspected more closely. Adjust the cham's lighting so the cage provides cooler shaded areas.
But there's no need to worry about me disappearing. I've been around to offer advice for almost 7 years now. Other vets have come and go but not me. There are a lot of people who either don't have an experienced reptile vet nearby or need to know a little bit more about what they might be dealing before they understand the significance of needing to go to the vet. I'm happy to offer guidance or advice where it can be useful. When I get a lot of messages I may not always get back to them immediately but I try to do so within a few days. I don't think my time is best spent on beginner type questions so some of those I'll refer back to the forums to make a general thread. There are lots of super helpful, very knowledgeable people to help with care and egg laying. 
Your appreciation of my efforts really means a lot to me though.
