Sorry to necro this thread but i'll just add my 2 cents for what it's worth.
I bought a used PS4 and right away I noticed it was running sluggish and i got poor framerate ingame, textures was also slow to load. It was getting hot but at least not shutting down. My first thought was the heat might be normal since it's been a few years since i owned a PS4. I reckoned the hdd could be faulty
What i tried:
# I re-initialized the PS4 thinking there is a lot of clutter on the hard drive from the previous owner but there was no improvement.
# I installed a spare SSD that was laying around. It ran a little better, the menu was less laggy but in-game there was no difference.
# Opened the PS4 halfway to clean it but didn't find a lot of dust. Cleaned the fan and heat sink anyway but no change.
# Completely took it apart and cleaned what little dust was left and changed the thermal paste making sure the thermal pads that was on the memory stayed in place. (Some of you with heat issues after redoing thermal paste might have dislodged the memory thermal pads causing overheating and shut down). No change after new thermal paste but i left the top cover off and then I noticed the fan wasn't speeding up while gaming, it was just spinning slowly.
# As a last ditch effort before calling the seller i took a old 1tb hdd that only had like 2 months run time on it and reinitialized the ps4 with it. Lo and behold the fan starting speeding up while gaming in reaction to the PS4 heating up and would slow down again as cooling happened.
So my assumption is that I had a faulty hdd to start with then put a faulty or incompatible SSD in which made no change. When i installed a healthy HDD everything was working normally. Steve from Tronicsfix on Youtube has mentioned in his videos that hard drives can cause some weird issues. I guess due to corrupt files.