The liquid thermal conductivity of the ionic liquid (IL), 1‐hexyl‐3‐methyl‐imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf2N]), saturated with compressed vapor and supercritical carbon dioxide was measured over three isotherms (298.15, 323.15, and 348.15 K) and pressures up to approximately 20 MPa using a transient hot‐wire technique. Pure [HMIm][Tf2N] thermal conductivity was also measured over a temperature range of 293.15–353.15 K at ambient pressure and with hydrostatic pressure to approximately 20 MPa. Literature vapor–liquid equilibrium data were used to predict the liquid CO2 composition at the conditions investigated. Initially, the liquid thermal conductivity slightly decreased with pressure/composition of CO2 followed by a gradual increase that is mainly attributed to hydrostatic pressure effects. Simple composition‐based mixing rules for mixture properties are not qualitatively nor quantitatively accurate. These data could be used to engineer heat transfer equipment required for a variety of proposed IL applications in CO2 capture, absorption refrigeration, biphasic CO2/IL reaction platforms, etc.