To better control the state of carbon dioxide during supercritical carbon dioxide drilling, a mathematical model is established to analyze the wellbore carbon dioxide temperature and pressure influencing factors. In this model, the influences of formation temperature change and fluid-friction-generated heat on wellbore temperature distribution are considered. Additionally, the impact of casing, tubing, and cement sheath thermal resistance on heat transfer are considered. The model is validated by comparing the wellbore temperature data calculated from this model with data from previous models. Based on the model, the factors that may affect the wellbore carbon dioxide temperature and pressure are analyzed. The results show that the downhole temperature decreases with the decrease in nozzle diameter and geothermal gradient, and with the increase in injection rate. The injection temperature significantly affects the wellbore temperature near the wellhead, but it does not affect the downhole temperature. Therefore, for low geothermal gradient formation, reducing the injection rate and increasing the nozzle diameter are two effective methods to maintain the CO2 at the downhole in the supercritical state. The pressure inside the coiled tubing increases with the increase in injection rate and decrease in nozzle diameter, but the injection temperature and geothermal gradient has little effect on the pressure inside both the coiled tubing and annulus.