When you use two words together to refer to a single action, such as referring to air-conditioning a house, jump-starting a car, or mass-producing a product, a hyphen is required. (The same is true regardless of the form of the verb: air-condition and air-conditioned

Air-conditioning, when used as a noun, is hyphenated. The house has air-conditioning.

Air conditioner, a noun, is open. I was riding in a bus with air conditioner.

Air-conditioned: Both as an adjective and a verb is hyphenated. The air-conditioned room. Air-condition a building.

I would say the translation does not change because of the hyphen.

Air is conditioned with an air conditioner.

Let me know if you have any doubts