Recently, ferromagnetic/non-magnetic heterostructures have been widely studied for the generation of terahertz (THz) emitter based on spin-to-charge conversion. Actually, thermal spintronics effectively combines thermal transport with magnetism for creating and detecting non-equilibrium spin transport. A spin current or voltage can be induced by a temperature bias applied to a ferromagnetic material, which is called spin Seebeck effect (SSE). In this paper, we present a SSE based THz emission by using the heterostructures made of insulating ferrimagnet yttrium iron garnet (Y₃Fe₅O₁₂, YIG) and platinum (Pt) with large spin orbit coupling. Upon exciting the Pt layer with a femtosecond laser pulse, a spin Seebeck current arises, applying a temperature gradient to the interface. Based on the inverse spin Hall effect, the spin Seebeck current is converted into a transient charge current and then yields the THz transients, which are detected by electrooptic sampling through using a ZnTe crystal at room temperature. The polarity of the THz pulses is flipped by 180° when the direction of the external magnetic field is reversed. By changing the direction of the pump beam excitation geometry to vary the sign of the temperature gradient at the YIG/Pt interface, the polarity of the THz signal is reversed. Fast Fourier transformation of the THz signals yields the amplitude spectra centered near 0.6 THz with a bandwidth in a range of 0.1–2.5 THz. We systematically investigate the influence of annealing effect on the THz emission from different YIG/Pt heterostructures. It can be found that the THz radiation is achieved to increase ten times in the YIG/Pt grown on a Gd₃Ga₅O₁₂ (GGG) substrate through high-temperature annealing. The mechanism of annealing effect can be the increase of the spin mixing conductance of the interface between YIG and Pt. Finally, we investigate the pump fluence dependent THz peak-to-peak values for the annealed YIG/Pt grown on the Si substrate. Due to the spin accumulation effect at the interface of the YIG/Pt heterostructure, the THz radiation intensity gradually becomes saturated with the increase of pump fluence. Our results conclude that annealing optimization is of importance for increasing the THz amplitude, and open a new avenue to the future applications of spintronic THz emitters based on ultrafast SSE.