The solubility of carbon dioxide in ionic liquids of type 1-alkyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl)imide ([C(n)mim][NTf2]) with varying chain length n = 2, 4, 6, 8 is computed from molecular dynamics simulations. By applying both Bennett's overlapping distribution method and Widom's particle insertion technique, we determine solvation free energies that are in excellent agreement with available experimental solubility data over a large temperature range from 300 to 500 K. We find that the Computed solvation free energy of carbon dioxide is remarkably insensitive to the alkane chain length, emphasizing the importance of solvent models with accurate volumetric properties. The simulations Suggest that the "anomalous" temperature dependence of the CO2 solvation at infinite dilution is characterized by counter-compensating negative entropies and enthalpies of solvation. By systematically varying the interaction strength Of CO2 with the solvent, we show that the negative solvation entropy Of CO2 is not caused by solvation cavities, but enforced by Coulomb and van der Waals interactions. We observe that solvation free energies and enthalpies obtained for models with different solute-solvent interaction strengths are subject to a linear correlation, similar to an expression that has been suggested for gases in polymers. Despite the apparent chain length insensitivity of the solvation free energy, significant changes in the solvation shell of a CO2 molecule are observed. The chain length insensitivity is found to be a consequence of two counter-compensating effects: the increasing free energy of cavity formation is balanced by a favorable interaction of CO2 with the alkyl chain of the imidazolium cation.