Is the temperature in a refrigerator constant or does it vary throughout the fridge?

The temperature will vary throughout the fridge, particularly after a fresh load is added. But even in 'steady state', the upper of the container will be warmer than the lower. For cold air sinks by virtue of its higher density.
It varies. It will be colder at the bottom than at the top. The temperature difference will only be 1 or 2 degrees at most.... Incidentally - the Word is 'does' - not 'dose' !