Temperature can affect the sound of an instrument in a variety of ways, which are different for each instrument. It also influences the abilities of a player. In the case of the violin, for example, warmer weather changes the amount of friction between the bow and the strings, changing the way the bow pulls on each string. Warm weather also tends to expand instruments and thus alter their ability to withstand tension, which again changes their interaction with a musician. In a piano, increases in humidity and temperature cause the bushings (hinges in the mechanical assembly of the piano action around which one component rotates with respect to another) to swell. Such swelling increases the time between when the player hits a key and when the hammer hits the string by roughly 10 milliseconds. Musicians describe this effect as "sluggishness."
Most temperature-related issues can be corrected by tuning either the actions (physical mechanisms that strikes the strings) or the strings themselves, adding lubrication in appropriate spots or just modifying the way the instrument is played.
Some musicians are convinced that cooling an instrument to extreme temperatures can change its tone as well. Trumpet and flute players have been known to freeze their instruments in -300 degree Fahrenheit "refrigerators" for a few days, describing the sound that comes out of the thawed instrument as "more mellow." In recent experiments, however, we did not find a noticeable difference in the sound following this type of treatment.
Answer originally posted on April 5, 2004.