  Monte Carlo simulations have boosted the numerical study of several different
physical systems and in particular, the canonical ensemble has been especially
useful because of the existence of easy and efficient relaxation algorithms
required to minimize the energy, the relevant extensive thermodynamic variable
appearing in the probability distribution, which drives the system after a
thermalization process to equilibrium. Nevertheless, the nature does not know
about statistical ensembles and therefore it is desirable and a theoretical
challenge to show how to perform efficient numerical simulations in the
microcanonical ensemble. In this article, we present a method based on the
concepts of configurational temperature estimator \cite{Rugh,GDP} and on
stochastic dynamics to do it. The method is independent of the Monte Carlo
update strategy, and can be implemented for both local update or cluster
algorithms. We illustrate the main features of the method by performing a
numerical simulation of the planar interacting classical spin system, known as
the two-dimensional XY-model.
