i think you will find that the anwer is chemical reaction, or more to the point chemical action.
as most "soap powders" contain enzymes (and other such wonderfully named things) they do not work when cold, a bit like asking you to to manual labour outside in the snow, you will do it, but you would feel / work better if it was a nice warm sunny day.
Incidentaly as enzymes are actually "alive" they are killed at 62 degrees, so doing a "boil wash" is really of no use.
A boil wash comes from days gone by when clothes were put in a thing called a copper, (my long gone granny had one in the kitchen) and the water was quite literally boiled, and along with ordainairy soap and a scrubbing board the clothes were cleaned
the action of a washing m/c serves only to agitate the clothes (which is why a drum (inside a washing m/c) has paddles and goes round slowly then stops and goes the other way) its the water going through the material that actualy lifts the dirt off, all the detergent does is to help break the dirt down,(then as i said the water lifts the dirt off) and the lather carries it away.
Modern detergents also have a "flouresing" agent that makes clothes look whiter than white, which is why if you leave paper money in your pockets when washed, when someone puts the money under a "forged money checker" the money will glow (flouress)
also if you notice some detergents are "non bio" that is really to say that they have no biological ingreadiants, and rely on various forms of "bleach" to clean clothes, and that is why non bios make coloured clothes fade
i bet you wish you hadnt of asked now.
incidentally leaving money in your clothes when being washed is a criminal offence........
it is more commonly known as money laundering.
one other thing Americans favour a top loader rather than a front loader m/c, it may be because with a top loader you can open the lid (m/c stops) and add more washing, but they use about 3 times as much water
joking aside all the above is true