Hello friend, Thank you for posting your question on Just Answer! I will be happy to help you with this problem.
This is a Panel problem and i would call and scream really, can you squeeze the panel at the edge and notice any difference,, And is it on ALL inputs such as dvd player also??
And being it happens once warm you can test the controller board.
Friend you have a thermo problem, Unit is showing a line after? Min. There is no one set answer for this issue, but there is a trick you can try that I use. And that would be to open the set, Turn on and use a hair dryer blow some heat on the controller board, this is the small board in the center of the Panel. Then the Signal board, Basically each board inside, The bad board will cause the line quicker than 10min, This is how you can Isolate the problem, And once you have order that board and you should be fine.
Well Good luck friend, and if my efforts on trying to help you save on those large labor charges are appreciated, feedback and a bonus will be appreciated