Summary: We consider the inverse problem of determining the time-varying strength of a heat source, which causes natural convection in a two-dimensional cavity. The Boussinesq equation is used to model the natural convection induced by the heat source. The inverse natural convection problem is posed as a minimization problem of least-square criterion, which is solved by a conjugate gradient method employing the adjoint equation to determine the descent direction. The present method solves the inverse natural convection problem accurately without a simplification of the governing Boussinesq equation.