TL;DR, I don't think APR's intake works as advertised and I think their claims are based on half truths and some BS. This is supposedly a company that takes pride in their R&D. For anyone who cares to know why the way I think, continue reading.
I can't explain why the OP's temps are that much higher, but I would say that wouldn't surprise me if the temps were at least as high as the stock intake. The reason why I say that is because by the looks of the location, the APR intake appears receiving mixed hot & cold air all the time. Even when the car is moving. I agree with the OP that their claim of "Intake Air Temperature Management" and "improving the pressure ratio" is complete BS. The picture and description on their website leads you to believe that there is a ram air effect, which there is absolutely none.
The APR intake is not taking the air from the same location because the stock setup routes the air from the grill that has slits to bring in fresh air. That being said, the engine compartment is a low pressure area and the bottom of the car is a high pressure area relative to the engine compartment and air moves from high to low. The question becomes, does the APR intake bring in more fresh air or more hot air from the engine compartment? The intake because of it sucking air in, is also by nature a low pressure area. I would guess that it may even be lower than the bottom of the car, thus sucking in all of the hot air. Also notice the stock air intake on the right side where the slits are in the grill. Stick your hand in there and feel what VW engineers did. In my opinion it is quite clever that they angle that plastic downwards. This (counterintuitively) creates an eddy which turns the airflow upwards into the ducting to the intake. This downward turned piece of plastic may also help create an even lower pressure to help suck in more air by way of venturi effect. It is quite apparent to me that VW has thought this through and that they intended to take in cold air from those holes in the top of the grill.
Yes, I realize that the back (towards the engine) of the intake ducting is open and no, I don't know exactly why VW decided to do this. I have a few theories. One is so the intake doesn't ingest foreign objects, such as rain. Two, maybe to reduce the amount of induction noise. Lastly, if the openings on top of the grill get clogged or so the airflow while the car is standing still is sufficient. I would guess that the majority of air that enters the stock intake while it is in motion comes from the openings above the grill.
The picture showing the low pressure vs high pressure appears to be misrepresenting what is happening. Ram air pressure is dynamic pressure, but the pressure in the stream of air is measured as static air pressure. The higher the velocity of air, the lower the static air pressure. Keep in mind that air moves from high to low pressure and that high and low are relative to each other. The air that is entering the intake should be labeled "Lowest Pressure".
Any smoker can attest to this because they have seen it in action when driving down the interstate. Crack a window open and watch where the smoke goes when you exhale. Out the window that has air rushing past it right?
For what its worth, I haven't seen a design yet that appears to be worthwhile to purchase. I could see how modifying the stock grill to have openings on the drivers side and either using the APR intake or opening up the intake on the stock ducting may give some gains on lower IATs or relief on airflow to the turbo. How much we don't know until people do some more 3rd party testing. I will also say that the less you "bend" the air, the more efficient the flow should be. APR has the upper hand there, but I think there needs to be a way of it bringing air in from the top of the grill.
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