An investigation was carried out to determine experimentally the thermal conductivities of non-Newtonian fluids in a shear field. Both time independent purely viscous and viscoelastic fluids were considered. A coaxial cylinder apparatus with a rotating outer cylinder was used to establish the velocity field in the test fluid. First, the thermal conductivity of distilled water measured to validate the instrument. The experimental water data agreed within 1% of literature values and there was no effect of outer cylinder rotation (shear field). However, for non-Newtonian fluids such as aqueous CMC and Separan solutions, there were significant increases in thermal conductivities of up to 70% for CMC and 50% for Separan depending on the shear rate, polymer concentration and temperature. Considering the shear rate dependent thermal conductivity in the study of heat transfer in non-Newtonian fluids could be important. As in natural convection, the momentum and energy equations could no longer be solved separately but would have to be solved simultaneously.