Transient conjugated heat transfer in circumferentially partly heated thick-walled pipes and minipipes with thermally developing laminar flows is investigated, involving three-dimensional wall conduction and fluid axial conduction. The problem is handled for an initially isothermal, two-regional infinite pipe, for which the upstream region is completely insulated and the downstream region is circumferentially partly insulated by considering an instant increase in the outer wall temperature of the other circumferential part in the downstream region. Solution is made numerically by a finite-difference method, and a parametric study is conducted to analyze the effects of four defining parameters, namely, the Peclet number, wall-tofluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio, and wall thickness ratio, on heat transfer characteristics. The results show that in both the wall and the fluid sides, besides backward heat transfer due to axial conduction, a large amount of heat is transferred because of angular conduction from the circumferentially heated to the unheated part of the pipe. Wall conjugation highly compensates the effects of partial heating and an important percentage of heat transfer to fluid is realized from the unheated circumferential part of the pipe. The results are also seen to be much affected by the parameter values.