We present a theoretical description of the almost temperature independent mobilities of photoinjected electrons or holes in discotic liquid crystals. Using data from band structure calculations on triphenylene-based systems, we calculate the electron and hole mobility using the framework of the stochastic Haken-Strobl-Reineker model. We show how almost temperature independent mobilities can be explained in two ways, either by assuming the fluctuations of the tunneling matrix element to be small or by combining the different temperature dependences of the different modes of molecular thermal motion.