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.
The TOTAL amount of heat to be removed (case and mobo plus CPU) is exactly the same in both Options. Hence the rise in temperature from room air to exhaust air is also the same. The initial temperature of the room air has no impact on that.
There is a VERY small difference between the options. Option 1 uses cooler air for rad cooling, and that is a bit more efficient. This has a small impact on the amount of air flow required (and hence fan speed and energy use) since most of the air flow is determined by the major heat source being cooled - that's the CPU chip. There also may be a small advantage to Option 1 when your workload is very high and the CPU is running near max temperature, because cooler air through the rad will help to keep the CPU cool.