Traditionally, the cheese is made early in the morning, the whole process starts while the cows are being milked. The cream is skimmed from the evening milk and added to the vat, then the morning milk is put directly from the cows into the vat (through a straining funnel) without undergoing any cooling. Once the morning milk is all added, the culture is added (whey) and it is warmed up and stirred thoroughly. Then, the evening milk is added. The evening milk is left in shallow pans called Gebse overnight, and as it get rather cold on the alp at night this milk will be 50 to 60 degrees. The idea is that the adding of this cooler milk should bring the milk pretty close to the target temp of 26 R, which is the temperature at which the rennet and culture work the best. The rennet is added to the milk as soon as it reaches the target temp.
If you are using refrigerated milk, and aren't working with a milking cycle, then you might do things a little differently. Instead, all milk can be added at once, heated to 26 R (91 F) and cultured, then after 1/2 an hour rennet is added. This should APPROXIMATE the conditions of the traditional process.