If you ever have to make a blind bet on that day's weather in Tucson, bet sunny, and you'll win more than 96% of the time. With 350+ days of sunshine a year, Tucson is one of the sunniest cities in the United States! That translates to fun events all year, sports and outdoor activities even in midwinter, and family-friendly weather that almost never gets in the way of things to do.
Apple Watch, its power adapter, and Apple Watch Magnetic Charging Cable follow applicable surface-temperature standards and limits. Even within these limits, sustained contact with warm surfaces for long periods of time might cause discomfort or injury.
My watch was displaying Cupertino weather although the weather app on iPhone was set to my city. It wasn't until the Watch app on iPhone was set my city did the Watch report the correct time. So if you travel I don't think the watch will 'automagically' report the temperature of the current city. I think you have to: a) add the city to the city list in Weather app on iPhone. b) change the city in the Watch app. I don't think there is a 'current city' setting, that changes as you travel.