To shed a different light on this: think of temperature as walking through mud. Your legs lose energy trying to slowly pull a lot of mud behind you. Now think about skiing. A lot less snow is dragged with you but it flies fast. Here, what is interesting is if one fusion reaction does happen, then the alpha (helium) particles leave at 2.9 MeV. After two collisions with protons, if the second proton they have hit hits…
This was actually a helpful analogy for me. I'll have to take your word on the accuracy of it, though.