Ideally, a thermal rectifier is a device where heat current preferentially flows in one direction, just as the electrical diode works for electrical currents. Herein, we introduce a design of a thermal diode based on the combination of first- and second-order phase transition materials. Validation is realized by a proof-of-concept device consisting of a hybrid composite of neopentylglycol (NPG) and gadolinium (Gd) as the first- and second-order phase transition materials, respectively. Device manipulates the heat via a combined effect of molecular transformations in NPG as well as deactivation of magnons in Gd at the transition and Curie temperatures, respectively. Thermal measurements of the hybrid thermal diode demonstrate a thermal rectification factor of 1.45, which is higher than the value obtained for the reference device based only on NPG. We interpret such enhancement in the thermal rectification factor due to the presence of an asymmetry temperature jump along the heat transfer axis of the device as a consequence of the impact of both phase transitions. Results are corroborated via finite element analysis of the diode by using ANSYS. Hence, such combination of effects has been proved as successful strategy to develop enhanced-performance thermal rectifiers.