How does the Apple Watch get the temperature?
Solution 1:
The temperature shown does come from the Weather App. Small bits of data on the watch face are known as complications.
Tapping the temperature on the watch face will open the Weather app thus revealing the source of the data. The watch gets the data from your iPhone which, in turn, uses location and data from the Internet. You may find more useful information in the Apple Watch User Guide.
Solution 2:
The Apple watch doesn't have a temperature sensor for external temperature.
It probably uses the same web service as the Weather app.