Molar conductivities, A, of dilute solutions of the ionic liquids 1-butyl-3-methylimidazolium chloride and 1-butyl-3-methylimidazolium tetrafluoroborate in methanol and DMSO were determined as a function of temperature (methanol, T = (273.15 to 313.15) K; DMSO, T = (293.15 to 318.15) K). The data were analyzed with Barthel's low-concentration chemical model (IcCM) model to obtain the limiting molar conductivities, Lambda(infinity)(T), and association constants, K(Lambda)(o)(T), of these electrolytes. From Lambda(infinity)(T), the Eyring activation enthalpy of charge transport and (where possible) the ion conductivity of the cation, lambda(infinity)([bmim](+)), were determined.