The carbon dioxide heat pump (CDHP) offers efficient heating over a wide temperature range, but its heating energy efficiency under low-temperature conditions decreases obviously due to a correlation with the evaporation temperature, limiting the widespread use of CDHP in cold regions. To address this, we implemented a passive solar house with short-term heat storage capacity to raise the evaporation temperature and studied it by experimental and theoretical analysis. We introduced the concept of contribution degree (K) of solar energy to the heating performance coefficient of CDHP. The prediction models for the evaporation temperature, heating performance coefficient, and K were constructed gradually. The study optimized the operation mode of solar-assisted CDHP using the evaporation temperature partition theory and presented a method to calculate the limit distribution range of K. The result shows that the order of importance level of the significant items on evaporation temperature was ambient temperature (Ta) > direct solar irradiance on the inclined surface (Gb) > scattering solar irradiance on the inclined surface (Gr) > GḃTa > Ta2 > Gb2. The predicted limit distribution range of K was [0.00, 8.17]. The study optimized the operation mode of solar-assisted CDHP into three categories. It was observed that K changes positively with any single variable according to the law of a composite function composed of a natural exponential function and a quadratic function. Our study suggests a feasible development direction and offers a new theoretical and engineering basis for overcoming the large-scale application limitations of CDHP in cold regions.