1 Hot stuff have their atoms move around faster. This results in them hitting the dirt harder, resulting in it dissolving faster.
2 For fairly complicated reasons solids dissolve better into hotter liquids (and gas the reverse dissolve better in cold liquids).
3 Additionally when you have certain solids to clean (e.g. fats) they tend to become more liquid like as they are heated up resulting in them not sticking to the surface as hard and are easier to wash away.
Theses three factors together result in dirt being taken off much better by hot liquids.
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