How will the difference between the readings of dry and wet thermometers

How will the difference between the readings of dry and wet thermometers change with decreasing air temperature, if its absolute humidity remains constant?

Formula for determining relative humidity:
F = (R / Rн) * 100%,
where R is the absolute density of water vapor,
Rн – the maximum possible density of water vapor for a given temperature.

With decreasing temperature, Rn decreases.
At a constant absolute density R, a decrease in Rn leads to an increase in relative humidity and a decrease in the intensity of water evaporation. If the evaporation rate is lower, the wet bulb will cool down worse. Its reading will differ less from the reading of a dry bulb thermometer.

Answer: The difference between dry and wet bulb readings will decrease.