Based on thermodynamics, heat transfer mechanisms, and fluid mechanics, a transient temperature and pressure coupling calculation model for supercritical carbon dioxide coiled tubing drilling is established in this study. In this model, the Joule-Thomson effect is considered, the CO2 physical properties are varied with the temperature and pressure, and the heat transfer in the wellbore and formation are both considered unsteady. The model is solved using the fully implicit finite difference method. The results show that the wellbore CO2 temperatures predicted by Gupta's model and Wang's model are both lower than that of the proposed model. The primary reason for this discrepancy is that the previous models considered the heat transfer in the wellbore as a steady state and ignored friction heat. In the shallower and deeper sections of the well, the wellbore temperature changes rapidly with the depth, whereas in the middle section of well, the wellbore temperature increases linearly with increasing depth. The wellbore temperature changes with circulation time, but the wellbore pressure is unaffected by the circulation time. The injection rate and nozzle diameter both have a significant effect on the downhole temperature and tubing pressure, and an injection rate that is too larger or a nozzle diameter that is too small may lead to CO2 that cannot exist in a supercritical state. (C) 2018 Elsevier Ltd. All rights reserved.