Forget momentum. Collisions don’t have momentum. The sum of the momentums of two particles that elastically collide remains the same after the collision. Nothing about energy here.
The energy of each molecule is proportional to the square of its velocity. Slow it down and it gives up energy, and the law of conservation of energy says the energy goes somewhere.
In a gas, molecular motion is its energy. The energy is felt as wind and heat. Wind is a net motion in some direction. Heat is random motion.
In our discussions we’re talking about a gas that’s at a constant pressure.
I am sorry but are simply making things up and ignoring basic physics. This has become a conversation of you claiming red is really blue.
I don’t care to find new ways to explain the same thing over and over.
Have a nice day.