Evaporative cooling during humid weather is obviously ineffective. Outside humid air when passed through a desiccant to absorb some of the moisture in it tends to warm up slightly due to some added heat from the desiccant.
Evaporation of water is always associated with cooling of the material, condensation of water vapor into a liquid means vice versa i.e., warming of that material.
Thanks Jan sounds convincing because a change of phase could be taking place with regard to the water vapour which is converted into water inside the molecules of the desiccant material.