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Not quite correct, liquid cooled engines also had cooling systems producing thrust.
They usualy used a ducted radiator for that as it allowed for a small duct, creating less drag.
As the radiator was relatively large and angled, the pressure diffrence was kept to a minimum.
However the temperature difference between theice cold intake air and warm/hot air meant a significantly higher volume of hot air exiting the converging duct at higher speed than the plane was flying at despite beeing at a lower pressure than at the entrance.
It works a more efficiently with liquid cooled engines as the duct can be designed more efficiently that way.
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