I think it might have something to do with condensation/evaporation? Not sure how it works though.
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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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