I got a new ps4 slim and had it on stand by most of the day. I woke it up and turn it off so I can move it. It has been 3 hours since I turned it off and it's hot to the touch still. Is this normal and if so why?

how hot it hot? just warm? fry an egg hot?

It should not be hot 3 hours after being turned off. Slightly warm is one thing but not hot.

But are you sure it's off and not doing things in standby? Is it still plugged in? If you unplug it does it get cool?

When I woke it up to turn it off it was downloading a patch still (slow internet) would that keep it on? I did unplug it and 30 mins later it was room temp.

Yes. Downloading a patch means that the machine is on. It's in a reduced power state and probably not using all its cores, but it's on, and that generates heat.

You might not have the greatest venting situation and you should maybe improve that (not sure what your set up is) but I wouldn't necessarily worry at this point. Sounds like it was just on doing some downloading.

Modern consoles, man. When an NES is off it's just off. Like...off.

vents are on the sides right? it was on a folding table laying down with nothing around it.

Hmm. Is the room hot? Is there any airflow?

Also this gets back to how hot is hot. If it was just a bit warm I wouldn't worry too much about it. If it was painful to the touch then maybe you should have it checked by a service center (though they'll probably say it's fine) or at least set up an external fan blowing on it so there's airflow in the room.