Microwave heating of pure alumina is studied experimentally and numerically, in a 2.45 GHz single-mode cavity, for different density levels. Even considering a constant incident power, the results show a complex evolution of the alumina temperature: first a two-step increase, then a maximum, and finally a cooling stage. In addition, a density dependence of the heating efficiency is observed: a more efficient heating occurs for lower densities. Using the effective medium approximation (EMA) to derive the physical data as functions of density, the numerical simulations are in contradiction with the experiments, proving that the EMA approach is not able to correctly predict the imaginary part of the permittivity. Furthermore, the simulations do not accurately describe the first moments of the heating, nor the long-term evolution of the temperature (cooling). We then explain the origin of this discrepancy: the need to adjust the movable stub on the one hand, and to account for heat exchange between the cavity and its surroundings on the other.