Capillary phase transitions (evaporation, melting, and sublimation) and the pore triple point of CO2 confined in MCM-41 mesoporous media with a pore diameter of 3.5 nm have been studied by using an isochoric heating procedure in a high-pressure low-temperature differential scanning calorimeter over a pressure range of 0.5-40.5 bar. The procedure is validated by the agreement between the measured conditions of bulk evaporation/sublimation and literature data. The main finding in this work is that the solid-to-fluid phase transitions of CO2 in MCM-41 shift to temperatures higher than those of the corresponding bulk phase transitions. It is also found that the formation of a solid phase of CO2 in MCM-41 does not require the presence of a liquid or solid in the bulk. The capillary-melting and capillary-evaporation curves approach each other as temperature decreases until they meet at the pore triple point. The effect of pressure on capillary melting temperature is significant at pressures close to the pore triple point. Furthermore, the capillary-melting curve approaches the bulk saturated vapor-pressure curve as temperature increases, thus hinting an agreement with the prediction by molecular dynamics simulation in the literature that the curves eventually intersect each other at a high temperature and pressure. Based on the measured capillary phase transitions, the pore triple-point temperature and pressure of nanoconfined CO2 are bracketed and found to be much lower than those of the bulk triple point.