In this paper, we discuss the molecular mechanism of the heat conduction in a liquid, based on nonequilibrium molecular dynamics simulations of a systematic series of linear- and branched alkane liquids, as a continuation of our previous study on linear alkane [T. Ohara et al., J. Chem. Phys. 135, 034507 (2011)]. The thermal conductivities for these alkanes in a saturated liquid state at the same reduced temperature (0.7Tc) obtained from the simulations are compared in relation to the structural difference of the liquids. In order to connect the thermal energy transport characteristics with molecular structures, we introduce the new concept of the interatomic path of heat transfer (atomistic heat path, AHP), which is defined for each type of inter- and intramolecular interaction. It is found that the efficiency of intermolecular AHP is sensitive to the structure of the first neighbor shell, whereas that of intramolecular AHP is similar for different alkane species. The dependence of thermal conductivity on different lengths of the main and side chain can be understood from the natures of these inter- and intramolecular AHPs.