TV turns itself off, and then switches back on with no display

Hi my name is Eric,
I hope I can help you with your issue ,
Sounds like an internal TV issue , only way to know is replace the power supply brick.
There are a few boards in the Tv none that are easy to buy, I'll bet you can buy a replacment power brick on ebay for less than $30.
If you do open the Tv look for any capacitors that look bulged or swollen.
example
　
　
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Thanks

Its normal for the 'brick' (power supply) to get hot, the power supply would not be the problem here as if it was faulty it wouldt power the screen at all, I guess you have a small 15" LCD TV which runs on 12V? The problem would be internal, Hitachi TVs have this problem, its normally down to a small capicitor on the main board. Speak the manufacturer for more info.