Ok, so the TV doesnt seem to have any fault if ran with the case back left off. This would have to indicate overheating and a safety threshold which is cause a power down rest period...would everyone agree?
The power supply is the only item within the TV which seems to get very warm other than the screen itself.
Sounds quite possible.
For those mentioning SOGA, I believe you can only go via this route if you can prove an inherent fault. Meaning you'd have to pay for an engineer to test your TV and confirm that fault will likely have existed from manufacturing and hasn't just developed. Have a check over on MSE's consumer rights board, there's always lots of threads on faulty TV's.