The development of nanocomposite materials with desired heat management properties, including nanowires, layered semiconductor structures, and self-assembled monolayer (SAM) junctions, attracts broad interest. Such materials often involve polymeric/oligomeric components and can feature high or low thermal conductivity, depending on their design. For example, in SAM junctions made of alkane chains sandwiched between metal layers, the thermal conductivity can be very low, whereas the fibers of ordered polyethylene chains feature high thermal conductivity, exceeding that of many pure metals. The thermal conductivity of nanostructured materials is determined by the energy transport between and within each component of the material, which all need to be understood for optimizing the properties. For example, in the SAM junctions, the energy transport across the metal-chain interface as well as the transport through the chains both determine the overall heat conductivity, however, to separate these contributions is difficult. Recently developed relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy is capable of studying energy transport in individual molecules in the time domain. The transport in a molecule is initiated by exciting an IR-active group (a tag); the method records the influence of the excess energy on another mode in the molecule (a reporter). The energy transport time can be measured for different reporters, and the transport speed through the molecule is evaluated. Various molecules were interrogated by RA 2DIR: in molecules without repeating units (disordered), the transport mechanism was expected and found to be diffusive. The transport via an oligomer backbone can potentially be ballistic, as the chain offers delocalized vibrational states. Indeed, the transport regime via three tested types of oligomers, alkanes, polyethyleneglycols, and perfluoroalkanes was found to be ballistic, whereas the transport within the end groups was diffusive. Interestingly, the transport speeds via these chains were different. Moreover, the transport speed was found to be dependent on the vibrational mode initiating the transport. For the difference in the transport speeds to be explained, the chain bands involved in the wavepacket formation were analyzed, and specific optical bands of the chain were identified as the energy transporters. For example, the transport initiated in alkanes by the stretching mode of the azido end group (2100 cm(-1)) occurs predominantly via the CH2 twisting and wagging chain bands, but the transport initiated by the C=O stretching modes of the carboxylic acid or succinimide ester end groups occurs via C-C stretching and CH2 rocking bands of the alkane chain. Direct formation of the wavepacket within the CH2 twisting and wagging chain bands occurs when the transport is initiated by the N═N stretching mode (1270 cm-1) of the azido end-group. The transport via optical chain bands in oligomers involves rather large vibrational quanta (700-1400 cm(-1)), resulting in efficient energy delivery to substantial distances. Achieved quantitative description of various energy transport steps in oligomers, including the specific contributions of different chain bands, can result in a better understanding of the transport steps in nanocomposite materials, including SAM junctions, and lead towards designing systems for molecular electronics with a controllable energy transport speed.