The conductive heat transfer through rarefied polyatomic gases confined between parallel plates maintained at different temperatures is investigated. The approach is based on three kinetic models namely the Holway, Rykov and Andries models, as well on the DSMC scheme supplemented by the Borgnakke-Larsen collision model. Results are presented for the total as well as for the translational and rotational parts of the heat flux and of the density and temperature fields in a wide range of the Knudsen number and for small, moderate and large temperature differences. The effect of the thermal accommodation at the boundaries is also examined for two diffuse-specular reflection scenarios at the walls. All three kinetic models provide results which are in very good agreement between them and they also compare very well with corresponding DSMC results. Comparisons with experimental results are performed verifying the validity of the simulations. The total heat fluxes of diatomic and polyatomic gases have been found to be about 30%-50% and 50%-75% respectively higher than the corresponding monatomic ones, with the highest differences occurring in the free molecular limit. The translational and rotational temperature distributions (as well as the total temperature) are very close to each other for each set of parameters examined and they are close to the corresponding monatomic ones, when the translational and rotational accommodation coefficients are the same. On the contrary they depart from each other when the two coefficients are different. In most cases as the gas surface interaction becomes more diffusive the dimensionless total heat flux is monotonically increased. However, for adequately large temperature differences and sufficiently high gas rarefaction levels a non-monotonic behavior has been observed. It has been also found that in polyatomic gases the dimensional heat flux is not necessarily increased as the molar mass is decreased, which is always the case in monatomic gases. (C) 2015 Elsevier Ltd. All rights reserved.