Overheating has produced leaking pixels on screen.

Hi there. So I left the phone out in the sun, got the warning message, and promptly took it inside to cool down. After a while I turned the screen on and a black smudge/dirty fingerprint was present on screen. It has been like that for a few days, im guessing the damage is permanent. The question is - what is damaged? Is it the lcd, the screen, or could it be fixed or cleaned by a competent technician? Also, how much would i expect to pay for any replacement parts? Thanks in advance.