Camera has been bad for a while so with nerves of steel and giant balls I ripped into the phone with guitar picks, a single screwsdriver, a laptop, 4 hours, and the tact or a surgeon.
Kind of seems to work. Will be some time before the thermal paste sets up. Here are some test images. They include a shot of the phone disassembled, but the phone itself is taking the picture. There is also a shot of the thermal paste used.
Subjectively it seems better. Darker shots look more like they did after a trip to the freezer with the thermal paste applied. Oh well best of luck.
e: couple hours later, phone has had time to cool somewhat. still not great in low-light, but definitely better (what was i expecting, a canon?). the minimum amount of light needed to take a picture of acceptable quality has lowered somewhat resulting in better quality photos from flash photography, or otherwise in less-than-ideal lighting conditions. a hot phone still seems to precipitate the worst of the malfunction, but overall the function is better with the fix. mission accomplished. i think that probably thermal paste is a much better solution than copper tape as well, personally, since the copper tape that was already there seems taut.
not any serious visible damage from the disassembly and reassembly process. didn't bother re-applying the tape, and the volume rocker isn't quite in the same place, but everything still works, and looks good. upper speaker is in a slightly different position, which was startling the first time i pulled down the notifications / quick settings, but really not a big deal. strange that the strength of the bonds from the front case to the rear case is stronger than that of the front case to itself, there's something wrong with that design. i use a battery case that provides some marginal bump protection, which the phone would probably needs (even without modification), though i also used the phone naked for some time... the phone once fell about 3.5 feet from a coffee table onto hard industrial carpet once and also did some damage to the front case speaker-screen seam/interface, on the bottom of the phone. little irritating, my fingers could feel it but it wasn't really visible. strange that the aesthetic appeal of the phone for me falls more to touch than to appearance. the inspire 4g was a brick compared to this thing, a makeup compact.
minor nicks and warped aluminum and plastic aside, using a slow-gentle touch with a guitar pick, a hair dryer, and some patient observation i managed to disassemble and reassemble without any of the serious mangling i've seen on youtube of the earliest dissemblers (or people who were in a panicked rush.) make sure the pick is in the right place, and give the glue time to separate. if you aren't making progress get in their at a steeper angle, you should get maybe 3-4 mm of pick stuck in each side. don't fret if the speakers don't separate from the rear-case like the rubber runners on the front case do, once you get the bottom speaker separated, apply force there and in short order the top speaker, the left case will come unbonded. i plan on revisiting the rocker too. the only bit i haven't tested is NFC, but i figure either it will be fine or i just won't use it, since it really isn't something i've got the opportunity to use much anyway.
so like this:
1.) apply plectrum between rear case and front case
2.) wedge it in until it sits comfortable
3.) slowly, like you're unzipping a glue zipper, move the pick further in from the volume rocker
4.) if you find the plectrum isn't far in enough (it will be expelled from the case with force) repeat step 1, only a bit deeper, and at a sharper angle towards the inside of the rear case
5.) repeat until all 4 sides of the case are no longer bonded.
this will take a while, but if you follow my advice it should minimize changes to the seams and bent plastic or metal. you can only move as fast as the glue comes off, if you try and move any faster then you're just going to damage the case, so just take your time. sorry, phone repair entrepreneurs.
shame that HTC didn't have the time to read the data sheet for this camera and do some basic thermal analysis before assembling this device. i'll probably stick with HTC though since their software isn't too malicious to just use or replace, their builds don't tend to be fragile, and also i respect a company that releases rap videos. anyway this sort of turned into a blog. keep calm and plectrum on.
e2: if you look at the picture of the inside of the phone, the GPS cable is disconnected. opened the phone again, lost a fleck of rubber runner just below the top speaker which is a shame and looks cruddy. the usb port isn't in quite the same place. i also bent the volume rocker slightly, though it still functions acceptably. anyway, camera still seems a bit better though i wish i'd squirted in more thermal paste. open this phone as little as you need to. the best way to fix this is probably a replacement camera module, instead of the thermal fix suggested in the OP, unless you just bought the phone, and it isn't doing it yet.