Neither cold not warm are great at killing bacteria. Greases though, are at the temperature border between solid and liquid (the difference between grease and oil is basically melting point above or below room temp) so warmer will lead to release of a lot more greases, and many soaps also work better at warmer temperatures for much the same reason (soaps are fatty molecules). Oil and grease trap particles (and bacteria) and serve as a food source for bacteria, so eliminating superficial grease is the objective of cleaning and the reason to use warmer water as a general thing.
Many modern soap formulations are designed to work well at lower temperatures so they function well in cold water. It took a bit of work finding detergents that do work well at lower temps though (like cold water detergents for clothes).
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