  We propose an extension of the nonequilibrium invaded cluster (IC) algorithm,
which reestablishes a correct scaling of fluctuations at criticality and also
self-adjusts to the critical temperature. We show that by introducing a single
constraint to the intrinsic quantity of the IC algorithm the temperature
becomes well defined and the sampling of the equilibrium ensemble is regained.
The procedure is applied to the Potts model in two and three dimensions.
