Pour the milk into a medium saucepan and heat over medium-high heat, stirring occasionally, until the milk reaches 180 degrees F. At this temperature, the milk will be steaming and starting to froth, but not yet boiling.
Pour the milk into a bowl and let it cool until it is between 110 and 115 degrees F. This is the temperature range needed to activate the yogurt cultures. Then whisk in the plain yogurt. Cover the bowl with a lid or some plastic wrap and wrap it in a few heavy dish towels.
Turn the oven on to any temperature, and allow it to preheat for one minute. Shut the oven off, turn on the oven light, and place the towel-wrapped bowl inside. Close the oven door and let the yogurt hang out in the warm oven for 8 to 12 hours. During this incubation time, you want the oven to stay warm (about 110 degrees), so you may want to check every few hours and repeat the one-minute warming cycle if needed. (I usually don't worry about this because I let my yogurt incubate overnight, and it works just fine.)
You will know the yogurt is done when it looks like yogurt, with some liquid on top. This liquid is called whey and needs to be drained off before you will have thick Greek-style yogurt. To do this, place a fine-mesh sieve over a large bowl. Line the sieve with some cheesecloth or a double layer of paper towels. Scoop the yogurt into the paper-towel lined sieve and cover it with some plastic wrap. Place it in the refrigerator for about 8 hours until the whey has drained off. (You can either discard the whey or use it in place of water when baking bread. It will keep in a sealed jar in the refrigerator for up to 10 days.)
Scoop the yogurt into a storage container, cover, and store in the refrigerator. Homemade yogurt will keep for about a week.