I see that you came around to look at my reply so I will give you your answer anyway , never mind my question above ;
This a typical case of weak/vented capacitors on the power supply circuit , when cold they take longer to charge and hold that charge until somewhat up to par so the TV's voltages will be adequate.
There could be a dozen or so of those capacitors to replace throughout the tv , not only on the power board by the way but the ones causing this cycling are definitely on the power supply circuit.
I wish I could say that you could just replace that board and everything will be fine but there was nothing easy with those older plasma TV's and the new board would need to be adjusted per the TV's date written internally
So this means that a repair shop would be your next step and you would be looking at no less than a $300 repair .
Now considering the age of the tv at 7 years old and the fact that you can get a new 50" tv with all the bells and whistles for around or less than $500 ,I would think twice before investing that kind of money into this one.
I think your money would be better invested in a new tv .
Let me know if you have other questions and if not then please do not forget to rate by clicking on the star icons at the top, then click on Submit so i get paid for my time helping you .
Also note that it will not close this post , you can come back here at any time if you need further info or help .