Is there a difference between 'air temperature' and 'temperature of air'?
I know about 'of' and how/when to use it, but I can't understand why 'air temperature' or something similar is right. Is it some kind of a rule? Or it is just an intuitive thing? :)

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The temperature is 20°C. (Colloquial. By default this would be understood to be the air temperature)
The air temperature is 20°C. (“Air temperature” refers to a certain meteorological measurement, so it’s more precise.)
The temperature of the air in my attic can reach 140°F. The temperature of the air in the freezer never exceeds -3 °C. (General. Note “the” air)

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Both phrases have the same meaning! It depends on how it is said in the conversation.

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Both are correct and mean the same thing, but air temperature is the most common way of saying it.

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Hello!

In my opinion, using "air temperature" is a better way of saying it as this is the compound noun. To say "the temperature of the air" is a long and clumsy way of saying it although that would probably be the direct translation from another language.

I hope this helps!