Does the sound of guitar strings change depending on the temperature? If you place the guitar in the freezer and later take it out will the sound be different? If you place it in the heater or blow hot air on the strings for a long time will the sound change?
Most materials, including guitar strings, shrink with cold. That means more tension and thus higher pitch. Of course, the guitar itself will shrink with cold too, but not as fast as the strings, because it has more mass and insulates better (being wood). Thus, what you will generally have, in the way of immediate tuning changes (there might be longer term effects also) is that as the guitar and strings cool down, you will first get higher pitch, then lower (as the wood shrinks). Warming up again, you will get lower pitch, then higher again.
I am not aware that anyone has done any experiments to test the extreme temperature changes you suggested. There is no practical application for the knowledge. A wood guitar must be kept out away from the harsh climate changes you suggest because of the potential damage to the guitar itself.
All wood contains moisture and all wood will expand and contract with temperature changes. Even the wood in your house will move as the climate changes. At my house certain doors stick during certain times of year but not others. Part of that may be due to temperature and part may be due to relative humidity.
Without testing my theory, I am going to say the sound of the strings themselves may not change that much due to being subjected to cold or hot temperatures. Of course if heated enough the strings would melt.
But the wood in the guitar is more likely to contract or expand and move based on temperature because of the moisture in the guitar reacting to the changes in temperature. Thus your guitar will go out of tune when exposed to a different temperature.
It is recommended that if your guitar has been out in a cold car in the case and you bring it into a warm house, that you should leave it in the case and allow it to warm gradually instead of suddenly. When I perform out and have to travel, I know I am going to have to retune when the guitar stabilizes at the temperature of the venue. The more extreme the difference in temperature, the more pronounced the effect seems to be on the tuning.
I am not sure why you need to know this information but it might be helpful to know that any change in sound may be as much a result of the guitar's reaction to the change in temperature as the strings themselves. From first hand experience and from my research on the subject, the guitar itself will actually react to the changes in temperature perhaps as much as (or more than) the strings might.
Yes, extreme temperatures will take away the factory temper of steel or bronze strings. They might still sound ok for a while but will sound deader quicker and get harder to tune. A string is only as good as the temper of the steel.