How lasting is this effect though compared to evaporative cooling (which lasts for as long as you stay hydrated due to the replenishment of moisture from sweat)? The volume of liquid you're adding to your garment can't be all that much, and if you combine your body heat with a high ambient temperature it seems like the water should reach equilibrium rather quickly.

I don't doubt it helps in the short term - I live in the southeast and I've done this when hiking many times (once my shirt's already soaked from sweat and I can find a cool stream) - but it only provides a temporary respite.