Low biogas yield in cold climates has brought great challenges in terms of the flexibility and resilience of biogas energy systems. This paper proposes a maximum production point tracking method for a solar-boosted biogas generation system to enhance the biogas production rate in extreme climates. In the proposed method, a multi-dimensional R–C thermal circuit model is formulated to analyze the digesting thermodynamic effect of the anaerobic digester with solar energy injection, while a hydrodynamic model is formulated to express the fluid dynamic interaction between the hot-water circulation flow and solar energy injection. This comprehensive dynamic model can provide an essential basis for controlling the solar energy for digester heating to optimize anaerobic fermentation and biogas production efficiency in extreme climates. A model predictive control method is developed to accurately track the maximum biogas production rate in varying ambient climate conditions. Comparative results demonstrate that the proposed methodology can effectively control the fermentation temperature and biogas yield in extreme climates, and confirm its capability to enhance the flexibility and resilience of the solar-boosted biogas generation system.