Now shipwreck is full of hot air.
Okay, that was a cheap shot, I admit it. But let me explain this to you as an engineer.
The 111F air coming out of the back of your PS4 is because the idea of modern cooling system design is to design your system so that the air coming out of the system is as hot as possible.
What, what? Did he really say that? Yep.
See, when you are talking about heating up and cooling, the key really is the total amount of heat generated and moved out of the box. The heat generated isn't controllable by the cooling system (not by much), it's just the amount of energy taken from the wall turned directly into heat. The key is how you get it out.
One way is to exhaust a fixed amount of air and the air temperature changes depending on how much heat there is to take out. You have to pick an amount of air (fan speed) which is enough air for even the most demanding (hottest) situations. The problem with this is the fan is going full blast all the time and for a system which dissipates 150W, full blast is going to be noticeably loud. This is why this is the "old way"of doing it.
The new way is to pick a temperature of air to exhaust and then exhaust a differing amount of air depending on how much heat you have to take out. The good part of this is that the fan is running at less than full bore when full cooling isn't needed. This is quieter and it actually takes less energy (which is just more heat you have to exhaust). So how do you pick a temperature? Well in a system of convective cooling the rate of cooling is based upon the difference between the temperate of the thing you are cooling and ambient. And for a given amount of heat to dissipate the amount of air needed goes down the higher you make the exhaust air.
So you pick a temperature the internal components are rated at and a temperature of air that is as high as possible but considered acceptable. And then you adjust the system to adjust up the airflow if the exhaust air is too hot or the internal components are too hot.
So Sony picked 45C for the exhaust air, which is 113F. That's why shipwreck measures 111F at the back of his unit.
But in the end, the exhaust temperature being higher doesn't indicate a problem putting this in an enclosed space, because you aren't measuring the volume of air too. It's really the input electricity that indicates how much this will heat up in an enclosed space. And well, it uses 150W, it's going to be about as intolerant of being in an enclosed space as the original Xbox 360 and PS3s were. My customized Ikea cabinet with active cooling which did a lot of work cooling my PS3 and original 360 but hasn't had much work to do lately will be working harder again with the PS4 on in there.