Yes. No. And depends. Temperature will remain the same as it is, for proteins, how the required doneness is controlled.
The time for cooking 10 2" thick steaks will be the same as the time for cooking 2 2" thick steaks of the same cut. So, in this respect scaling down doesn't impact the time.
However, if you're cooking a 3" x 3" x 4" chunk of meat for a roast for 2 people and the recipe is using a 6" x 6" x 10" chunk of the same cut, then you may need to adjust the time. (The numbers are merely to give you an idea.)
If you were making pot de creme and the recipe uses 250 ml wide necked mason jars and you decide to make smaller serves and use 125 ml jars then adjusting the time would depend on how the jar dimensions vary. If the jar is smaller diameter but fills to the same depth, then probably not. But if the jar is smaller in all dimensions then probably yes.
So, over all, the simple response is no. But you can see this is not always going to be the case.