No. The heat transfer from the hot air is a few Watts, I seem to remember 20- I worked it out, but over a very short period of time. It is a fraction of a Joule/ ftlb so don't worry about it. The heating due to friction between the moving surfaces will be higher. Airguns are pretty big chunks of metal so it would take a lot of energy to warm it up.

Not sure if Jim has stuck a springer in a freezer to see if they work at -20.