  An estimator for the dynamical temperature in an arbitrary ensemble is
derived in the framework of Bayesian statistical mechanics and the maximum
entropy principle. We test this estimator numerically by a simulation of the
two-dimensional XY-model in the canonical ensemble. As this model is critical
in the whole region of temperatures below the Berezinski-Kosterlitz-Thouless
critical temperature $T_{BKT}$, we use a generalization of Wolff's uni-cluster
algorithm. The numerical results allow us to confirm the robustness of the
analytical expression for the microscopic estimator of the temperature. This
microscopic estimator has also the advantage that it gives a direct measure of
the thermalization process and can be used to compute absolute errors
associated to statistical fluctuations. In consequence, this estimator allows
for a direct, absolute and astringent test of the ergodicity of the underlying
Markov process, which encodes the algorithm used in a numerical simulation.
