Results of an analytical study on the heat flow rate in two-dimensional heat-conduction problems are presented. For conduction problems which satisfy some symmetry properties it is proven that the heat how rate does not depend on the shape or dimensions of the geometry. For these problems the heat flow rate can be calculated without solving the distribution of the diffusing quantity. For the general problem it is shown that there is always a line which intersects isolines at a constant angle. Numerical results are presented to show the significance of the developed concepts.