The article describes a mathematical model of heat transfer in developed laminar flow in prismatic channels of rectangular and triangular cross-sections, including the equation of fluid motion and the energy equation with boundary conditions of the second kind on the channel walls. The analytical solutions for the velocity field have been derived from the equations of liquid motion. Solution of the energy equation has been obtained by numerical method of finite differences. The computational algorithm was based on the difference scheme approximating the boundary value problem, based on five-point pattern. This algorithm implements programs allowing calculation of the velocity and temperature fields in the channels and determination of the local and average heat transfer characteristics. In future we plan to build an algorithm and to develop a program for the numerical solution of the problem of convective heat transfer in channel of more complex geometry with projections on the walls.