Abstract We have investigated numerically the dependence of the temperature span and optimum operating frequency of solid state magnetic refrigerators on the most important physical properties of magnetocaloric materials. We concluded that the temperature span depends inversely on the thermal conductivity of the magnetocaloric material and is proportional to the square root of its density, heat capacity and maximum adiabatic temperature variation upon the application/removal of a magnetic field ( Δ T a d m ). Also, and contrary to general belief, the increase of the thermal conductivity is not the only factor able to increase the optimum operating frequency. Reducing the density, heat capacity, Δ T a d m or broadening of the Δ T a d ( T ) curve can result in larger operating frequencies. Our results show that a compromise between the maximum achievable temperature span and optimum operating frequency must be reached, as the increase of one reduces the other.