We study the temperature distribution of a power‐law fluid in a pressure‐driven axial flow between eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible, and fully developed flow for an adiabatic core and an isothermal outer cylinder (Eq. ). We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power‐law exponent n. The temperature is a strong function of the gap between the cylinders. Finally, dimensionless maximum temperatures are plotted to help pipe manufacturing engineers prevent excessive heating during production. POLYM. ENG. SCI., 53:2205–2218, 2013. © 2013 Society of Plastics Engineers