Abstract Mode-locked single-soliton state micro-comb (SSC) can be achieved in a miniaturized highly compact platform by pumping the micro-resonator with a single-frequency continuous wave laser. However, a significant challenge lies in effectively exploring the tuning range of pump power, spanning over hundreds of mW, as well as the detuning range and tuning speed in the range of hundreds of MHz and the order of MHz/s to GHz/s respectively. Here, we delve into a simulation model, considering thermal effects to ensure that the simulation accurately reflects the power drop and thermal detuning observed in the experimental process. Our simulation model, featuring precision scanning and iterative parameter demonstrations, has proven instrumental in accurately exploring the optimal tuning range for the existence of SSC to a few MHz. This provides a foundation for controlled and predictable SSC generation experiments.