Did you ever notice the little nuances of the little temperature gauge in this menu? Wearing a piece or two of either cold-resistant or heat-resistant clothing will remove one or two units of cold or heat respectively on the gauge.
You can see in Pic #2 that one unit of the hot side of the gauge is gone, and in Pic #3 you can see that two units of the cold side of the gauge are gone. That’s what clothing and food/elixirs do for the temperature gauge.
What’s different is when you have a fire or ice weapon equipped, or you’re carrying a lit torch. A fire weapon will cause the gauge’s needle to rise, as you can see in Pic #2 (which is near the River of the Dead on the Great Plateau, where it’s cold). The opposite is true if you have an ice weapon equipped.
A lit torch, however, does not affect the gauge whatsoever, as you see in Pic #1. The gauge indicates that Link should be cold, but he isn’t actually. Also, it’s worth noting that while a fire weapon is good for only one level of cold protection, a torch works for one or two levels.
One more little tid bit... If you do not have the Sheikah Slate, the temperature gauge just isn’t there!
I just find this stuff fascinating!