The transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow, is studied. This conjugated heat transfer process is characterized by the simultaneous thermal interaction between the wall tube and the adjacent thermal boundary layer of the power-law fluid. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluid is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the axial heat conduction effects are taken into account. The governing equation is reduced to a integro-differential equation which is solved by muliple-scale analysis and a conventional numerical technique. The results for the temperature of the wall tube and the corresponding average temperature are plotted for differents parameters such as conduction parameter, a, the aspect ratios of the tube, epsilon and epsilon(0) and the index of power-law fluid, n. (C) 2003 Elsevier Science B.V. All rights reserved.