Engines do work when chemical energy is changed from:

In a combustion engine, chemical energy is first converted to heat to cause the expansion of a fluid which then produces motion. In contrast, motor proteins are molecules that can convert the chemical energy released from adenosine triphosphate (ATP) hydrolysis directly into useful mechanical work.

If the water vapor content stays the same and the temperature drops, then the relative humidity increases. its vise versa.if the water vapor content stats the same and the temperature rises, the relative humidity decreases. so, yes, i'd say that temperature and humidity have a strong relationship.