The conjugate gradient method is used to solve the inverse problem of determining the spacewise variation of an unknown applied wall flux for laminar flow inside a parallel plate duct. One of the walls is insulated. The inverse analysis is based on the temperature reading taken inside the fluid at several different locations along the flow. The inverse analysis is performed by using the combination of the regular and modified conjugate gradient methods. The combined method was found to be more accurate than either of these two methods alone.