The inverse problem of determining wall heat flux from temperature measurement within the flow is investigated. The Boussinesq equation is used to model the natural convection caused by the heat flux at the bottom wall of a rectangular domain. The inverse problem is posed as an optimization problem which is solved by a conjugate gradient method, employing the adjoint equation to obtain the descent direction. This method solves the inverse natural convection problem accurately without a priori information about the unknown function to be estimated.