The Wigner theory for multichannel thermal transport has become a new theoretical paradigm for studying glassy materials like polymers beyond the classic phonon-gas theory. Although thermal transport in bulk polymers can be enhanced by aligning molecular chains, the role of heat carriers in polymers remains obscure. In this work, using the state-of-the-art Wigner theory, diffusions and locons are found to contribute significantly to the total thermal conductivity of disordered and aligned polymers due to coherence between proximate modes. Strikingly, locons contribute remarkably, 43 and 54%, to the total thermal conductivity of disordered and aligned polymers, respectively, due to their high generalized velocities and generalized lifetimes. Interestingly, some locons in aligned polymers form propagative wave packets with ultralong mean free paths (MFPs) and become efficient heat carriers, which is supported by the high spatial extent of locons along their wavevectors. The thermal conductivities of both polymer models increase with temperature due to increased generalized specific heat and agree well with theoretical and experimental data. This work unveils the unique transport behavior of diffusons and locons, providing new avenues for the thermal management of polymer-based electronics packaging and the rational design of organic electronics, optoelectronics, and thermoelectrics.