right, you don't need a constant temperature to make yogurt.
in india, people don't even measure the temperatures as you mentioned.
we just boil the milk (to sterilize it), let it cool some amount, put in the curd (indian english term for yogurt, dahi in hindi, thayir in tamil) starter (which is just curds from a previous batch), mix, and leave it covered for a while, typically overnight, anywhere in the house, or in a cooler or warmer part, depending upon your location and ambient temperature. the milk automatically sets, by the action of the bacteria, and becomes curd.
nothing to it. even kids can make curd.