Transient conjugated heat transfer for thermally developing laminar flow in thick walled pipes is analyzed involving two-dimensional wall and axial fluid conduction. A two-regional, initially isothermal pipe is considered and the problem is handled for hydrodynamically developed flow with periodically time-varying outer wall temperature in the downstream region. The problem is solved numerically by a finite-difference method and a parametric study is done to analyse the effects of four defining parameters namely, wall thickness ratio, wall-to-fluid conductivity ratio, wall-to-fluid thermal diffusivity ratio, the Peclet number and also the effect of angular frequency. Considerable amount of heat is transferred through the upstream region due to both wall and fluid axial conduction. Heat transfer characteristics change periodically in time similar to the periodic change in the outer wall temperature. The results are found to be affected by the parameter values and by the angular frequency.