Experimental measurements are presented of the hole mobilities of four conjugated discotic systems, forming columnar liquid crystals, as a function of temperature. The measurements cover the crystalline/glassy phase and mesophase of these materials. It is a remarkable fact that the mobility is almost independent of temperature in the range 30 degreesC-170 degreesC. Various explanations of a weak temperature dependence exist and these are explored. They include the small polaron of Holstein in the nonadiabatic limit and the effect of the dynamic disorder present in the system. (C) 2001 American Institute of Physics.