Transporting waxy crude oils through long pipelines at low temperatures may be challenging due to its paraffinic components which lead to a complex (yielding) rheological behavior depending on the flow and thermal history. In order to evaluate those characteristics MRI velocimetry tests were performed with an equivalent model waxy fluid with macroscopic behavior analogous to waxy crude oils. This local flow data associated with stress measurement provide information on the effective fluid properties independently of possible flow heterogeneities. Here the rheological behavior of this fluid was observed for cooling under different shear conditions and for various flow histories at constant temperature. We show that after a significant destructuring it exhibits a yield stress fluid behavior with a low yield stress and some very slight thixotropy. However these rheological characteristics are strongly and irreversibly dependent on the maximum flow rate to which the fluid has been submitted after cooling, whatever the shear history during cooling is. In particular it exhibits a high apparent yield stress for cooling under low shear but, if it is then sheared at a higher shear rate, it will flow under much smaller stress whatever the subsequent flow history.