Would it be possible to have a sunburn from hot air instead of the sun?

Not really : Hot air or steam can produce a thermal burn for the high temperature just like exposure to hot water which can produce scalding burns. A sunburn can occur on a cold day and is the result of ultraviolet rays which pierce the skin surface . If your under an umbrella on a hot day and have uv protective clothing you won't get burned. Hot air and uv rays are different forms of energy.