The behavior of uniformly heated plates is considered for the situation where a patch is adhered over a region of the structure. A variational formulation results in a self-consistent set of equations and conditions, which governs the response of the system. The nonlinear problems are solved analytically, yielding exact results within the context of the mathematical model employed. A stability criterion is established for the class of problems considered, based on the second variation of the potential energy of the composite structure, and issues of stability are assessed in this context. Three non-dimensional parameters that characterize the response of the structure are identified. These are a `loading parameter', a `critical temperature' and a `critical membrane force'. Results of numerical simulations are presented for various loading and support conditions, patch lengths, and mechanical properties of the components. It is seen that bifurcation buckling, `asymptotic buckling', and `sling-shot buckling' are all possible scenarios for the class of structures of interest.