If I were using store bought pasteurized milk, I'd heat it up and re-pasteurize it before adding the cultures (after cooling it first.)
I'm using raw milk and for a reason....it is more digestible for my cranky system. So I make sure I don't heat the milk higher than about 115, as 118 will start to kill the beneficial enzymes. If the milk is clean and fresh and raw, the multiple redundant systems within the milk will successfully compete with pathogenic bacteria and keep them at bay. The yogurt cultures will boost this effect. The yogurt will be runny and will need to be strained if a thicker yogurt is desired, however, there are many uses for that lovely, live whey.
I use the picnic cooler method and use quart jars of milk. Homemade yogurt from raw milk will keep for weeks in the fridge, so I make 8-9 quarts at a time and store it right in the one quart jars that I made it in. Easy-peasy. I heat the milk in the jars in a sink full of hot tap water. My tap water comes out of the faucet at 120 F so it is perfect. I also preheat the cooler with tap water, and once I put the jars of milk in it, I fill the surrounding spaces with more tap water and insulate the cooler with blankets and pillows from the couch and then go to bed. In the morning...yogurt!