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If air of a certain temperature blows through a car radiator (or a computer case), what effect will air humidity (non-condensing) have on cooling rate?

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The cooling effect of air will depend in the flow rate and thermal conductivity of air. The latter is in turn a function of temperature, pressure and water content. Counter-intuitively, if we keep pressure constant, the most water the less thermal conductivity, and the decrease in thermal conductivity is more significant for higher temperatures, as shown by the following graph:

enter image description here

A more detailed explanation of the causes of this behavior can be found at the original source of the image: electronics-cooling.com

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The fins don't have moisture so no difference from evaporative cooling there.

Air with higher humidity has a higher capacitance. As humid air passes from the front the back it will adsorb the same amount of heat and temperature at the trailing edge will be lower than the dry air. So humid air will maintain a greater temperature difference which results in more heat transfer. You should never have condensing as the air is being heated.

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