In the past two decades, simulated annealing has played an important role in stochastic reconstruction of porous media. In this study, we compare simulated annealing algorithms constrained by low-order microstructural descriptors and controlled by four annealing schedules that use different ways of temperature reduction. Besides the plain exponential decay of temperature, three adaptive schedules deducing the optimum cooling speed from statistical measures, such as mean system energy and standard deviation of energy, are investigated. Unlike the first three schedules, which modify temperature by a stepwise manner, the fourth one takes into account the effect of move generation strategies and decreases temperature continuously maintaining quasi-equilibrium. The performance of the algorithms is exemplified by reconstructing pore structures of five porous samples. The fourth annealing schedule can significantly reduce the total time required for the reconstruction process itself and for parameter tuning because the same values of annealing parameters are used for both 2D and 3D reconstruction. None of the schedules affects the quality of the reconstructed pore structures.