My normal routine is based on absolutely nothing I have read -- it is just what I started doing, and it seems to work fine, so I continue:
I fill my cheesemaking pot with filtered, non-chlorinated water and add any utensils I will be using, then put on the lid and put it on the stove on high to bring to a boil. As it is heating, and while it boils for 10 minutes or so, I put the milk, still in the plastic jugs, into the sink and fill the sink with the hot tap water. (My tap water only goes to about 120˚ F, so not all that hot.) This begins warming up the milk, maybe from 40˚ F to 60˚ or 65˚ F. Once the pot is sterilized, I empty it, put the sanitized utensils on a sanitized counter, and pour in the milk. I fill a larger pot with hot tap water, put the cheespot in, and set it all on the stove. At that point, the thermometers go in (one for the milk, one for the outer water) and I begin bringing to desired temperature.