It does. You can even do a similar experiment to see how it works. Fill a milk jug with water, freeze it, set it in front of a fan, turn the fan on, the air in front of the fan will feel cooler with the ice than without it. You can see the condensation gather in a puddle at the bottom and once the jug has warmed up, it will no longer have an effect at all. Global warming causes the polar ice caps to slowly melt and evaporate, it cools the air, the air blows, it mixes with the hot extremes, and wildness ensues like hurricanes, monsoons, and major storms. Once the cooler temp has dissipated you're back to your new normal - which on average is still hotter than usual.