Seems to be more the Controller, have you tried to force reset the PS4? Try to pull the power cable let it sit for a bit and turn it back on and try again. If anything trouble shoot with another controller, Easier and cheaper for new controller than new console.
If you’re Transmission is overheating I would suggest to look up on YouTube your card year and model “How to check Transmission fluid” And than take it to your local trusted repair shop if possible. A Transmission “Cooler” is not a real thing sadly.