"Another hazy, hot, and humid day in the south."
Humidity affects temperature whenever the distribution of water molecules isn't in equilibrium. To understand what I mean by this equilibrium, let's examine a simple situation: a puddle of water on a bathroom counter. The puddle doesn't appear to be changing, but we need to look at its surface microscopically. There at the surface, water molecules are landing and leaving all the time. If the rate at which water molecules leave is equal to the rate at which they land, then the puddle is neither growing nor shrinking and is in equilibrium with the moisture in the air. That balance between leaving and landing water molecules is the equilibrium I have in mind.
With the water and air in equilibrium, humidity issues won't have any effect on temperature. But suppose that the air's humidity is too low to maintain the equilibrium balance. In that case, water molecules will leave the puddle more often than they'll land and the puddle will gradually shrink. To break free of its neighbors, each departing water molecule must gather together more than its fair share of the water's thermal energy, so as the puddle evaporates the remaining water becomes colder. Water molecules leaving the cooling water less frequently, so after a while the puddle is again in equilibrium-water molecules leave and land at the same rate. But now the puddle is colder than before.
On the other hand, suppose that someone is taking a shower and the air's humidity is high. Now water molecules land on the puddle more often than they leave. As each extra water molecule lands on the puddle, it binds with other water molecules and releases thermal energy. The puddle grows during this condensation process and also becomes hotter. The rate at which water molecules leave the warming water increases, so pretty soon the puddle is again in equilibrium. But this time the water is hotter than before. As you can see, changing the air's humidity can change the temperature of wet objects.
Answered by Lou A. Bloomfield of the University of Virginia.