I don't know the answer, but what you suggest is probably there or there abouts, and a combination of things
As for PCPs not being affected, the opposite is true, primarily due to the increased potential energy of the pressurised air. This leads to an increase of approximately 1.3fps increase/decrease per degrees centigrade change in typical UK conditions. It will vary per gun, but it's always there, and it's a well documented fact. No idea why springers have not had the same focus though, perhaps someone can shed light on it?
James