It's when I discovered yeast rinsing/washing that I realized yeast are living organisms, and the success to good beer is with happy yeast. I really didn't know much about homebrewing until focusing on the yeast.
- The purpose of boiling the water is to keep the yeast's food as pure (sterile) as possible, so their output (beer) will be pure, also.
- The purpose of cooling the water is to keep the yeast comfortable.
- The purpose of dumping the water into the carboy is to separate the LIVE yeast in the liquid from the DEAD yeast and other inanimate trub.
- The purpose of refrigerating that yeasty liquid is to put the yeast to sleep so you can separate it from the "dirty" liquid that contains output of some of the former recipe.
- The purpose of cooling the wort is to, again, keep the yeast comfortable.
- The purpose of gradually warming the refrigerated yeast slurry to room temp is because that's what temp the wort will be for the most part... you want them as close as possible, so as to minimize shock.
Remember... yeast are people, too, man!!