How does the ozone layer affect the temperature of the stratosphere?

The gas molecules in the ozone layer are shattered by absorbing the energetic radiation from the Sun. This makes them hot, and establishes a temperature profile. This profile is what set this layer of the atmosphere apart from those on either side of it. If it were not for the action of the ozone layer, there would be no stratosphere, likely just troposphere right up to ionosphere. If our Sun cooled so it made little or no UV-C, that is what we'd have.