Soret coefficients of aqueous phosphoric acid and aqueous iodic acid are determined conductimetrically at 25 °C. As the molality of phosphoric acid drops from 0.05 toward 0.00 mol kg−1, the enthalpy of transport jumps from 2 to 15 kJ mol−1. For iodic acid, a stronger electrolyte, the corresponding increase is smaller, from 12 to 17 kJ mol−1. Equations are developed for the enthalpy of transport of 1:1 weak electrolytes. The equations are used to evaluate the reactive enthalpy of transport and the intrinsic enthalpies of transport of the ionized and molecular forms of phosphoric and iodic acids. Equating the enthalpies of transport of the acid molecules and the acid anions provides estimates of single-ion enthalpies of transport. Thermal diffusion measurements are reported for potassium dihydrogen phosphate and potassium iodate to help interpret the results. Keywords: thermal diffusion, enthalpy of transport, Soret coefficients, weak electrolytes, phosphoric acid, iodic acid.