Due to the existence of a continuous (percolating) network of weak interparticle bonds in a liquid, wax suspensions can behave as "soft breakable (brittle) solids": under the action of either a large stress over a short time or oscillating low stress (fatigue test), the initially solid network of these materials is broken and dispersed in the liquid, which turns them abruptly ("collapse") and irreversibly to a low viscous fluid. Here we show that the rheological behavior of these materials is not only impacted by the temperature but also by the history of the temperature. The elastic modulus and the yield stress increase when the temperature is decreased. The data for different concentrations (ranging from 7 to 50 wt% of wax in oil) and temperatures (as a function of the distance to the critical temperature) fall along a master curve, which shows some equivalence between temperature and concentration. More surprisingly, the elastic modulus in the linear regime and the yield stress are dependent on the minimum temperature the material has experienced during its preparation. As a consequence of these different characteristics, an original rheological behavior so far essentially observed with very different materials (metals) results, namely thermal fatigue: when the material is submitted to temperature cycling (small temperature amplitude test), the material progressively weakens during each elementary thermal cycle and can finally "collapse" after a sufficient number of cycles, i.e., the elastic modulus in the linear regime decreases from 10(6) to 10(3) Pa. These findings could have implications in the start-up flow of waxy oils in pipelines since with the help of this technique, the material strength (e.g., the yield stress) and consequently the pressure required to resume the flow can be reduced considerably just by imposing thermal cycles.