In the present study the development of mixed convective flow is studied in a helically coiled heat exchanger with an axially varying wall temperature for Re = 500, Pr = 5 and d = 1/14 and compared to the constant wall temperature boundary condition. In the method used the parabolized equations are solved using a finite difference discretization scheme. The influence of buoyancy forces is analyzed on heat transfer and secondary flow. For all Grashof numbers studied it appears that both heat transfer, quantified by the Nusselt number, and secondary flow, quantified by the relative kinetic energy, exhibit a wavy behaviour in axial direction. For higher Grashof numbers, however, this phenomenon diminishes for the case with an axially varying wall temperature due to stabilizing stratification effects.