The combination is practically unrelated except for WOT conditions. Stock intakes flow plenty cfm for daily driving rpm's and are already "cold air". As a matter of fact some CAIs actually increase intake temp by pulling in more air from the engine compartment.

Thus, theres really nothing magical about the "combination". Only caveat is if the CAI changes the IAT mount to a location that doesn't provide an accurate reading. As long as the temp reading is good, the computer will adjust for a/f ratio.