Imagine a spinning fan impeller at a constant speed, you can see the amount of airflow churning out by it does not change regardless of temperature, or rather how dense the air mass is. Even though the air entering it is very much stretched, air mass particles are dispersed apart in between the void, in “volume” term, of which airflow is measured, it is constant. This explains why is temperature is not a variable of airflow in Fan Law.

If this is confusing to you, you need to know that air, unlike water, is compressible and thus expandable. Its density changes significantly by temperature, pressure and altitude. When pressure rises, the same air mass is represented by lower volume and airflow. This explains why high pressure roots blower has smaller outlet than inlet. Temperature rise has similar effect as expanding the air mass apart as lower pressure.

Back to the spinning wheel. As temperature rises, although airflow is constant, air mass flowing through is not. This becomes clear that fan output pressure is a factor of temperature, as seen in Fan Law again.

That was about pressure generated by fan, pressure at the duct system too changes by the temperature. This pressure is friction against duct wall as air mass travels through it. Diluted airflow naturally incurs less friction.