This paper presents a computationally efficient novel heuristic approach for solving the combined heat and power economic dispatch (CHP-ED) problem in residential buildings considering component interconnections. The proposed solution is meant as a substitute for the cutting-edge approaches, such as model predictive control, where the problem is a mixed-integer nonlinear program (MINLP), known to be computationally-intensive, and therefore requiring specialized hardware and sophisticated solvers, not suited for residential use. The proposed heuristic algorithm targets simple embedded hardware with limited computation and memory and, taking as inputs the hourly thermal and electrical demand estimated from daily load profiles, computes a dispatch of the energy vectors including the CHP. The main idea of the heuristic is to have a procedure that initially decomposes the three energy vectors’ requests: electrical, thermal, and hot water. Then, the latter are later combined and dispatched considering interconnection and operational constraints. The proposed algorithm is illustrated using series of simulations on a residential pilot with a nano-cogenerator unit and shows around 25−30% energy savings when compared with a meta-heuristic genetic algorithm approach.