FeRh has been demonstrated to be an important material for the observation of magnetic phase transitions, such as the first-order transition from an antiferromagnetic (AFM) to a ferromagnetic (FM) state, in response to changes in the temperature. This is because of the magnetic moment induced in Rh atoms above the magnetic phase transition temperature. In the present study, we focus on the longitudinal spin Seebeck effect (LSSE), which involves the generation of spin voltage as a result of a temperature gradient in FM materials or FM insulators, and experimentally assess the effect of the crystalline quality of FeRh films and the properties of the substrate on the LSSE thermopower during the FM-AFM phase transition. The measured LSSE thermopower of an epitaxial (110)-oriented FeRh film grown on an Al2O3 substrate is approximately 60 times higher than that of a polycrystalline FeRh film on a SiO2/Si substrate. This can be explained by the high magnetic sensitivity and superior FM properties of (110)-oriented epitaxial FeRh films. Furthermore, by comparing the transverse thermoelectric voltage for in-plane magnetized (IM) and perpendicularly magnetized (PM) configurations, we quantitively evaluate the contribution of the exclusive anomalous Nernst effect (ANE) to the LSSE signals in the FeRh/Al2O3 structure, finding it to be approximately 15-30% over a temperature range of 75-300 K. LSSE measurements in Pt/FeRh films are thus demonstrated to provide a versatile pathway for the development of thermoelectric power generation applications and other practical spintronics and neuromorphic computing devices.