Intramolecular energy transfer in polymer molecules plays a dominant role in heat conduction in polymer materials. In soft matter where polymer molecules form an ordered structure, the intramolecular energy transfer works in an anisotropic manner, which results in an anisotropic thermal conductivity. Based on this idea, thermal energy transfer in lipid bilayers, a typical example ofsofi matter, has been analyzed in the present study. Nonequilibrium molecular dynamics simulations were carried out on single component lipid bilayers with ambient water. In the simulations, dipalmitoyl-phosphatidyl-clioline (DPPC), dilauroyl-phosphatidyl-choline (DLPC), and stearoyl-myristoyl-phosphatidyl-choline (SMPC), which have two alkyl chains with 16C atoms for each, 12 C atoms for each, and 18 and 14 C atoms, respectively, were used as lipid molecules. The thermal energy transfer has been decomposed to inter-and intramolecular energy transfer between individual molecules or molecular sites, and its characteristics were discussed. In the case of heat conduction in the direction across the membranes (cross-plane heat conduction), the highest thermal resistance exists at the center of the lipid bilayer, where lipid alkyl chains face each other. The asymmetric chain length of SMPC reduces this thermal resistance at the interface between lipid monolayers. The cross-plane thermal conductivities of lipid ntonolayers are 4.8-6.5 times as high as the ones in the direction parallel to the membranes (inplane) for the cases of the tested lipids. The overall cross-plane thermal conductivities of the lipid bilayers are reduced to be approximately half of those of the monolayers, due to the thermal resistance at the interfaces between two monolayers. The lipid bilayer of SMPC with tail chains of asymmetric length exhibits the highest cross-plane thermal conductivity. These results provide detailed information about the transport characteri.'itics of thermal energy in soft matter, which are new materials with design flexibility and biocompatibility. The results lead to their design to realize desired thermophysical properties and functions.