It sounds like maybe the tv is going into shut down. The tv has a built in safety circuit that shuts down the tv if it senses a problem. Usually it is a high voltage or horizontal circuit failure. It could be a power supply problem also. My suggestion would be to contact an authorized service technician, unless you are very familiar with electronics and have some test equipment, you would probably not be able to repair your self. I wish I could tell you exactly what is wrong, but there are too many things that cold cause your symptoms. Sorry for your troubles. Good luck
Kind of hard to say, this would be only a guess. If it is the power supply circuit, it could be a electrolytic capacitor going bad, this would be in the $150 dollar range. If it were a component in the horizontal / high voltage circuit it could be a high voltage transformer ($200-$250) or even a intermittent shorted crt picture tube, in which case would run in the $400 range. One thing: Does your tv show any signs that it is going to shut off, or is it doing anything out of the ordinary. Another thought is it could be a loose solder connection on the circuit board, which would be $75 to $100 repair. Please let me know any details.
If it is a temperature related problem, I would then lean more towards a power supply problem or a loose solder connection. If you decide to have it looked at by a technician, be up front with them and state that you really want to repair this tv but if it is going to run too much you will purchase a new one. I would not tell them you are willing to put $xxx into the repair, as then they might try to spend all that for you. I am not saying all technicians would do this, but some will. If you look for a tech that has a low checking or estimate charge, then he has to do some work to make some money, which in turn means he will probably find the problem fairly quick and give you an estimate. Where as if a tech charges a high checking charge he could just show up and say it going to cost $500 for repair, knowing you will not repair it, and leave with the checking charge and not really doing much work. Hope this makes sense, and good luck with the repair. Again, I am sorry I can not diagnose your problem to a T, but there are just too many variables working over the internet. Let me know if you need further assistance.