Polymers exhibit physical properties intermediate to those of elastic solids which follow Hook\u27s law and those of viscous fluids which behave according to Newtonian shear law, therefore, they are designated non-Newtonian fluids. Under a steady shear, non-Newtonian fluids exhibit not only the shear rate dependent viscosity but also their thermal conductivity changes with shear. It is the purpose of this paper to report on our investigation on the dependence of thermal conductivity on shear rate. Aqueous solutions of Carbopol 940 have been used as test fluids to investigate the effects of temperature and shear rate on thermal conductivity