Does yogurt maker keeps object at optimal temperature maybe around 40 centigrade, or current temperature of object?
There are a variety of ways to make yogurt. One that might be "easy" would to use a thermal cooker (giant thermos flask) if you happen to already have one, which would be under the "maintain temperature" (actually temperature will fall, but slowly) classification - but if you already have one, it's no extra cost or equipment needed.

Others have a thermostat and heater, but it's rarely an adjustable thermostat. I am currently using a dehydrator which is adjustable as my temperature control device; I have in the past used an oven with a standing pilot light (not adjustable, but a good temperature.)

Regardless of which type you use, you need to cool the milk (after scalding) to 35-40c before adding the yogurt culture (a small amount of any yogurt with live culture) or you will kill the culture - so you can't just dump 80C milk into "whatever" and expect yogurt, regardless of temperature controls or lack of temperature controls.

My research and personal testing W.R.T. the tradeoffs of time and temperature has lead me closer to 35C (for up to 24 hours) than 40C as a default setting. On the other hand, some go as high as 45C.