Cold air will have a slight increase in performance over hot air, for your sail purposes its irrelevant.
Concise enough )
Measuring wind speed, It all starts with Kinetic energy = 1/2mv² and apply the principles of Impulse turbine.
https://learnmechanical.com/difference- ... n-turbine/
Atmospheric air is not in a sealed container so sometimes its reaction to external energy is counter intuitive, for instance, in a sealed container if heat is added to the contents the pressure will increase, not so in a container-less environment.
Wind flowing down along a valley is a classic example of Bernoulli's theorem relating to static and dynamic pressures. Houses explode during tornadoes and hurricanes due to steep pressure gradients, very low pressures behind the structure (leeward side) created by aerodynamic forces literally pulls the structure apart, a structure can be designed to withstand the (windward) Kinetic energy the problem is the intense Low pressure created behind the structure, if there's no means of equalising the pressure differential along with weak structural strength, boom a major suck job.