Summary The cold acclimations of mesophyll conductance (gm), bundle‐sheath conductance (gbs) and the CO2 concentrating mechanism (CCM) of C4 plants have not been well studied. Here, we estimated the temperature response of gm, gbs and leakiness (ϕ), the amount of concentrated CO2 that escapes the bundle‐sheath cells, for the chilling‐tolerant C4 plant Miscanthus × giganteus grown at 14 and 25°C. To estimate these parameters, we combined the C4‐enzyme‐limited photosynthesis model and the Δ13C discrimination model. These combined models were parameterised using in vitro activities of carbonic anhydrase (CA), pyruvate, phosphate dikinase (PPDK), ribulose‐1,5‐bisphosphate carboxylase/oxygenase (RuBisCO), and phosphoenolpyruvate carboxylase (PEPc). Cold‐grown Miscanthus plants increased in vitro activities of RuBisCO and PPDK but decreased PEPc activity compared with warm‐grown plants. Mesophyll conductance and gbs responded strongly to measurement temperatures but did not differ between plants from the two growth temperatures. Furthermore, modelling showed that ϕ increased with measurement temperatures for both cold‐grown and warm‐grown plants, but was only marginally larger in cold‐grown compared with warm‐grown plants. Our results in Miscanthus support that gm and gbs are unresponsive to growth temperature and that the CCM is able to acclimate to cold through increased activity of PPDK and RuBisCO.