Whether or not our room has hot air does not change the results. Look at it this way.
Option 1: CPU radiator and its fans are arranged to draw in room air, remove from the liquid in the rad some heat, and deliver air at a slightly higher temp inside your case, where it is used to absorb more heat from the mobo before being exhausted.
Option 2: Other case fans arranged as intakes draw room air into the case and that cools the mobo etc, warming up the air. CPU radiator and its fans are arranged to exhaust air from inside your case, using that pre-heated air to remove heat from the liquid in the rad. Because this air is warmer than your room air, this will require slightly more air volume flow (faster rad fan operation) than in Option 1...