For comparison, here are results from a model that considers air temperature, humidity, atmospheric pressure, and even CO2 content, applied to D5 on a Feadog Mk 1. I chose D5 rather than G5 to reduce the impact of playing tendencies: I expect most of us would play that note somewhat close to the breakpoint to the second register.
If we adjust D5 to be in tune at 27 C, 100% R.H., around 300 m above sea level, 40,000 ppm CO2:
At 27 C, 100% R.H., same elevation, 400 ppm CO2, D5 will be 16 cents sharp.
At 27 C, 50% R.H., same elevation, 400 ppm CO2, D5 will be 11 cents sharp.
At 20 C, 50% R.H., same elevation, 400 ppm CO2, D5 will be 12 cents flat.
At 20 C, 100% R.H., same elevation, 40000 ppm CO2 (assuming we could obtain air like that), D5 would be 25 cents flat.
At sea level, all the results might theoretically be a fraction of a cent sharper, but any such effect would be totally buried by other slight differences in measurement.
Note that the impact of the change in CO2 content is as significant as using cooler air, and in the opposite direction. In the grand scheme of things, these are not huge differences in tuning.