Keeping the temperature stable around 40C helps the bacteria you want and keeps a healthy yoghurt culture. 
Too much hotter and the bacteria will die- too much colder and other bacteria will take over.
I have made yoghurt without a thermostat using a thermos flask and starting it at about 43 degrees C then wrapping the thermos in a blanket and putting it in the sun - in hot weather (28C plus) this has worked as it keeps the yoghurt culture at a stable enough temperature long enough. It takes 5-6 hours for the yoghurt culture to convert the milk to yoghurt. 
A thermostat makes it easier and more consistent.
Given the price of store bought live yoghurt you can save a lot by making your own.

Solomonsatoshi

food_and_drinks

Make your own fresh yoghurt ~ even when you travel!

Thanks for sharing, I remember my grandmother making yogurt when I was a kid, and I've never made it myself. 
I don't remember that she kept track of the temperature, I remember that it was just put in the oven and couldn't be touched until the next day. 
Can you tell me why it's important to control the temperature? 
I want to do more things at home and depend less and less on the store, this could be one of them...