We report the thermal control of a dissipative Kerr microresonator soliton comb via an optical sideband generated from an electro-optic modulator. Same as the previous reports using an independent auxiliary laser, our sideband-based (S-B) auxiliary light also enables access to a stable soliton comb and reduces the phase noise of the soliton comb, greatly simplifying the set-up with an auxiliary laser. More importantly, because of the intrinsically high frequency/phase correlation between the pump and S-B auxiliary light, the detuning between the pump and resonance frequency is automatically almost fixed, which allows an 18 times larger "effective" soliton existence range than the conventional method using an independent auxiliary laser, as well as a scanning of the soliton comb of more than 10 GHz without using microheaters.