Efficient triplet exciton emission has allowed improved operation of organic light-emitting diodes (LEDs). To enhance the device performance, it is necessary to understand what governs the motion of triplet excitons through the organic semiconductor. Here, we have investigated triplet diffusion using a model compound that has weak energetic disorder. The Dexter-type triplet energy transfer is found to be thermally activated down to a transition temperature TT, below which the transfer rate is only weakly temperature dependent. We show that above the transition temperature, Dexter energy transfer can be described within the framework of Marcus theory. We suggest that below TT, the nature of the transfer changes from phonon-assisted hopping to quantummechanical tunneling. The lower electron-phonon coupling and higher electronic coupling in the polymer compared to the monomer results in an enhanced triplet diffusion rate.