Hello , my name is Jack Perhaps I can help you with this problem but first i would have a few questions;
Once it shuts off , can you turn it back on and it lasts for another 15 to 20 minutes or do you have to let it cool down ?
Did this problem start suddenly/overnight or gradually got worse ?
I have t leave it off for a while. the longer it's off it may stay on for 20 minutes. it started overnight
And it usually takes approx. the same time 15 to 20 minutes before it shuts down ?
How is the picture prior to shut down , is there any signs on the screen before it does ?
no so,e times after it's been off only 10 minutes it may only stay on for 5. the picture doesn't seem as clear as before
O.k then in any case this does sound like a thermal problem , that is a component failure when it reaches a certain temperature.
Right now it would be difficult to say in which section of the tv this component might be located but usually this occurs in circuits that work the hardest and generate heat.
That would be the power board , the convergence board and the horizontal deflection circuit.
In any case this will require some serious troubleshooting and for that type of failure , it is difficult to troubleshoot at home as these circuits have to be monitored over a length of time until the cause can be narrowed down to a circuit then a component.
I`m afraid that to have a repair shop come at home to repair this, you are definitely looking at no less than 300 to $400.
If you go for the repair shop option then click on the link below and enter your zip code ;www.tvrepairpros.com
This will give you a list of repair shops in your area.You could give a call to different shops in your area to get an idea of their rates , this is a bit like buying insurances , it pays to shop around.
Wish i had better news and an easier solution for you today but i hope this help and I will be in standby if you have any questions.Thank you and please take the time to rate my answer if that answers your question and you can still reach me here at anytime after this chat is closed if you have other questions.
Please note that from where i`m sitting there is just so much that i can do and if you are going to rate my answer below O.K service then please do not rate at all , just let me know.