  By contrasting the performance of two quantum annealers operating at
different temperatures, we address recent questions related to the role of
temperature in these devices and their function as `Boltzmann samplers'. Using
a method to reliably calculate the degeneracies of the energy levels of
large-scale spin-glass instances, we are able to estimate the
instance-dependent effective temperature from the output of annealing runs. Our
results show that the output distributions of the annealers do not in general
correspond to classical Boltzmann distributions. For the small fraction of the
instances for which classical thermalization takes place, we find that the
effective temperatures are significantly higher than the physical temperatures.
Our results in this regime provide further evidence for the `freeze-out'
picture in which the output is sampled from equilibrium distributions
determined at a point in time earlier in the quantum annealing process. We also
find that the effective temperatures at different programming cycles fluctuate
greatly, with the effect worsening with problem size. We discuss the
implications of our results for the design of future quantum annealers to act
as efficient Boltzmann samplers and for the programming of such annealers.
