I'm afraid that TV repair shops don't exist anymore.
Modern electronics cannot really be repaired and nobody does this outside of warranty or OEM partners. If you really think the issues are simple overheating, try running both TVs outdoors (including power supplies if any) with the casing removed and see if they stay on for longer. If that is the case, get a laser thermometer and take readings of various areas of the internals and determine what is hotest. It may simply be a few overheating mosfets or something. If that is the case, get some heatsinks and thermal expoxy and attach them to the overheating parts.
Google the models and see if others have had the same issue. Post questions on DIY electronics forums like
http://www.electro-tech-online.com/r...r-electronics/
Most of these things have to be fixed by yourself. I don't think any companies specialize in this sort of thing anymore.