As I understand it AC units, fridges etc work by the compression of a gas into a liquid which then absorbs energy (heat) as it boils back into a gas. Air doesn't become a liquid under 300 bar of pressure so I wouldn't have thought it would cool an ASA.
If you take the example of the first automag RT's the valves warmed up under high rates of fire increasing the velocity meaning you had to chrono lower than you wanted to shot by about 30 fps,they later changed the valves to aluminium so they wouldn't get so hot.