I'm not a physicist, so this comment is made with some diffidence - but I suspect the most important factor here is the way the speed of sound is affected by temperature. It rises by about 0.6 metres/second for every degree Celsius rise. In an enclosed space, such as your piano room, the sound waves reaching your ear are not just those coming directly from the instrument, but also those reflected off wall, ceiling etc. Changes in the speed of those waves will minutely affect the the sequence of temporal intervals separating those direct and various indirect sources as they reach you. The brain interprets these changes, too small to be themselves directly perceptible, as a change in 'tone'.