How does the Apple Watch get the temperature? The Apple Watch shows the temperature on the clock face. 

When my Apple Watch is disconnected from my iPhone, the temperature display becomes disabled, but the time is still displayed. That leads me to think the watch doesn't have a temperature sensor, but it getting it from the Internet. 

My question is: How does the Watch get the temperature?
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.