Using multi-physics simulations, this study compares the temperature distributions, modulation efficiencies, and transient responses of a thermo-optical phase-shifter across three thin-film lithium niobate (TFLN) waveguides equipped with different heating circuits. The results reveal that the TFLN thermo-optical phase-shifter exhibits optimal modulation efficiency when the heating circuit is installed directly above the central waveguide. Alternatively, heating circuits with multiple resistors yield similar modulation efficiencies with reduced thermal crosstalk, making them particularly suitable for localized modulation in scenarios necessitating the integration of multiple waveguides. Three-dimensional multi-physics simulation results demonstrate a reasonable thermal modulation efficiency (approximately 34 mW) of the thermo-optical phase-shifter with a transient response time of approximately 180 μs.