Not so. First off, I generally measure exhalation, not inhalation. Second, I can regulate the exhale to a very small trickle through my pursed lips, and it will be dramatically cooler than a hard exhale with mouth wide open.
I suspect that there’s something related to the venturi effect going on, that the air compresses going through the pursed lips, and expands as it exits the “nozzle”. I know Cecil disputes this, but the feels like temp is dramatically different, regardless of airflow. It’s about pursing vs not pursing rather than exhalation power.
I am temped to dig up a thermocouple and try to measure the output.
That would be a fascinating experiment. Using a dry thermometer would eliminate evaporative cooling effects, something skin is particularly susceptible to and a possible source of the perceived cooling you mention.
Of course, exhalation isn’t dry either… so I wonder of exhaled water vapor would make a difference in the two air jets?