Cold water is generally the same temperature throughout the pipes, it’s not cooled at any point.
Hot water needs to travel from the water heater to the faucet it’s coming out of. In the process of that, all the “room temperature” water is being expelled from the pipe. If the faucet has been used for hot recently it’ll happen faster.
Cold and hot come from two different pipes, so with hot your basically waiting for he temperature to equalize across the pipe.
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