I think it might have something to do with condensation/evaporation? Not sure how it works though.
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Hot water has more energy to lose to get to room temperature so the change is more noticeable. You don’t sense temperature you sense difference in temperature.
Water can only get down to 32F and still be liquid it can get all the way up to 212f and still be liquid. The greater change on the hot end is more noticeable. That doesn’t make hot water cool faster it’s just more noticeable when something hot cools than something cooler than room temperature warming up to room temperature
“Cold” water might be just a few degrees above freezing. Room temp is only 30-40 degrees away.
Hot water (or something like coffee) could be anywhere from 130-210 degrees. Room temp is up to 130 degrees away.
Even if the 150-200 degree water cools faster (and it does), it has a lot further to go to reach room temperature.
If you have two metal cubes and start them at the same temperature difference, for example 10C and 30C cubes in a 20C room, they will reach room temperature at the same time.
When you have water, this is a different story because like you mentioned there is evaporation happening. In a regular room setting, water will produce a tiny amount of steam even if the water is nowhere near boiling. (Think about a small drop of water on a plate after washing your dishes, if you leave them overnight it will dry on it’s own). Water is essentially always boiling a tiny tiny bit. Still, the higher the temperature, the more it evaporates.
When water evaporates it has to first change from liquid to a gas. This doesn’t happen for free (see “latent heat” for more info), and requires a bit of energy. This energy comes from the rest of the water left behind, so the remaining water is a little bit cooler. The higher temperature water evaporates more, so it cools down a little bit faster.
Condensation also occurs, but for a slightly different reason. When the air is cold, the air becomes dryer. Near a cold surface like a cold window in the winter, the air might get so cold that as it dries the water vapor in the air returns to a liquid. This only happens when the surface is cold enough and the air in the rest of the room is humid enough. IF this is true, then the cold water will warm up slightly faster due to the opposite effect, but my hunch is still slower than the hot water.
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