I think we are consolidating two positive impacts of the cowl intake, and that is confusing the discussion. I can only speak to my experience with the Hemi, but I believe the same idea applies to the 4.0.
Cowl Induction (or any true cold air intake) does two things, both related, but each means something different to the PCM. First, the air is cooler. Second, the cooler air is more dense (meaning it contains more oxygen molecules by volume). On the surface it seems like the same thing, but temperature and density mean different things to the PCM. Density drives mixture, temperature drives timing - in simple terms, anyway.
When I first built the Hemi, it needed to have it tuned before I could drive it at all. To get it tuned quickly, I slapped an air filter right on the intake - like this:
I thought it would be fine for the tune - especially with the hood open. But it was not. This mill makes heat better than it does just about anything else, and the IAT's were exceeding 250. Seeing those IAT's, the PCM immediately pulled timing to avoid detonation (the hemi also has knock sensors which the 4.0 does not, but I think the end result it still the same. It pulls timing.).
As I recall, in this configuration it made a little less than 350 hp at the wheels. Less than I was expecting. The heat impact was such that the tuner could not get a good tune. He was able to make it drivable, but the hot air charge was certainly limiting power.
To address this, I added the cowl intake (as shown below) and went back to the same tuner and his dyno.
In this configuration the IAT's went from the 250 temps down to not too much above ambient. My tuner was then able to get a good tune. With just the addition of the cowl intake and much cooler air, it added 40 or 50 ponies at the wheels. All because the PCM was not pulling timing to protect the engine.
So technically the cowl intake by itself does not make more horsepower, but it does keep the PCM from seeing under-hood heated IAT temps, pulling timing, and limiting its power.
The increased density of the cooler intake air charge does make a bit more power, but not much at all by itself in the 4.0 as has been discussed. But in my case at least, the overall impact of the cowl intake was significant.