Climatic variables have major effects on all components and processes of the global carbon (C) cycle, including soil C contents and dynamics, which in turn have significant feedback effects on the global climate. We have investigated the interactive effects between soil C and projected climatic changes using the Institute of Numerical Mathematics Climate Model (INMCM) climate–C cycle model coupled to three soil organic matter dynamics models [the Lund–Potsdam–Jena (LPJ) soil biogeochemistry, ROMUL and Q models] based on three markedly differing conceptual interpretations of soil organic matter transformation (biochemical, discrete succession and continuous quality, respectively). According to simulations using all these couplings the positive effect of CO2 fertilization on plant productivity outweighed the negative effects of increased soil temperature on soil C, consequently soils were projected to contain 10–104 Pg more C in 2100 than in the preindustrial period. However, the projected soil respiration rates tended to be higher and additional C storage lower when the LPJ soil biochemistry model was used rather than either the ROMUL or Q models. Global temperatures for 2100 predicted by the INMCM coupled to either the ROMUL or Q models were almost identical, but 0.4 °C lower than those predicted by the INMCM coupled to the LPJ soil biochemistry model. The differences in global predictions obtained with the ROMUL and Q models were smaller than expected given the fundamental difference in their formulations of the relationship between the quality and temperature sensitivity of soil organic matter decomposition.