Yes, a PS4 can overheat. If it does you will see the red light come on and it will beep three times and shut off.
If it is just hot and the fan is running high, that's normal if you are playing a game that requires a lot of CPU/GPU power.
It sounds like where you have it is just fine. I would check to be sure that the vents are not dirty or plugged. If it's not dirty and it gets plenty of air flow then I wouldn't worry about it...especially since you said it gets cooler as it runs. This doesn't sound like anything to worry about.