Generalized theoretical results for heat transfer in laminar pipe flow with power law varying thermal conductivities are presented. The study is motivated by experimental observations that above a threshold shear rate the effective thermal conductivity for disperse two-phase mixtures increases with shear rate. Using a relatively general three parameter power law model for conductivity as a function of shear rate, heat transfer results for short and long pipes as well as with developing thermal profiles were obtained for both the uniform wall heat flux and uniform wall temperature conditions. The results show that significant enhancement in heat transfer coefficient could be obtained from the microconvective effects.