PS4 Overheating, Shuts down without beeps
So my PS4 from what I can work out is overheating. I turn it on and can leave it on the home screen for hours but as soon as I put it under heavy load, such as playing a game it shutdown without any beeps. Ive noticed the back right of the console get very hot (where the power cable gets plugged into the power supply) so Im assuming it the power supply but just want to double check before purchasing a new power supply. I have already cleaned the system out and replaced the thermal paste.
UPDATE: The ps4 seems to randomly try and restart itself.. When I try load a game or something it will beep and than all light will go off and then Ill here 2 clicks and the light will come on and than turn off