Based on the law of thermodynamics, this study establishes a numerical calculation model for the temperature and pressure of a carbon dioxide (CO2) injection well. Our model assumes that the well structure has a three-layer casing completion, and that the heat generated by the fluid friction losses is absorbed by the CO2 and tubing according to a contact coefficient. The heat transfer in the wellbore and formation is considered to be transient, and the model is solved using a fully implicit finite difference method. The results of numerical experiments show that the CO2 pressure and temperature are significantly affected by the injection rate, injection temperature, and tubing roughness. Therefore, it should be possible for engineers to adjust the injection temperature or injection rate to ensure that the CO2 reaches the super-critical state at the downhole. Although the Joule-Thomson effect and frictional heat proportional absorption effect also influence the CO2 pressure and temperature, they can be neglected at the engineering scale. (C) 2018 Elsevier Ltd. All rights reserved.