All that is well and good. But, the formula quoted proves there is an extremely small amount of change as the temperature of the string rises (0.004% per degree Celsius). That may be significant when going from 0 to 30 degrees, but that's not what we're talking about. It might be interesting if we could test this theory on ukulele or classical guitar strings. No one has established what temperature changes these strings experience, if any. It is possible, as the player's fingers contact them the warmth of the fingers and the friction between the fingers and strings raise the temperature. But, this would be extremely slight, and only in the very small areas where the fingers contact the strings. All other factors being equal, my guess is the temperature change across the length of a string could not be even that one degree, possibly not anywhere near one degree. That's not taking into consideration the movement of the string as it vibrates. This interaction with the air likely would have some cooling effect, and this would take place across the entire vibrating portion of the string. Again, so slight you would never notice, but the strings might actually be cooling as we play. We may have a formula and a theory or two, but we don't have the science.
The thing I said was preposterous is the notion that strings will re-tune themselves. The general tuning may go up or down on its own, under certain circumstances. But as it does, it goes out of tune. When reversal of these circumstances causes the tuning to go in the other direction (down or up) it also goes out of tune. The relationships between the strings are always changing, and the factors that change these relationships are incapable of making the calculations necessary to tune the instrument. A monkey couldn't tune you ukulele. It's ridiculous to suggest that a change in humidity (or temperature) can.