Combined heat, and power dispatch promotes interactions, and synergies between electric power systems, and district heating systems. However, nonlinear, and nonconvex heating flow imposes significant challenges on finding qualified solutions efficiently. Most existing methods rely on constant flow assumptions to derive a linear heating flow model, sacrificing optimality for computational simplicity. This paper proposes a novel convex combined heat, and power dispatch model based on model simplification, and constraint relaxations, which improves solution quality, and avoids assumptions on operating regimes of district heating systems. To alleviate mathematical complexity introduced by the commonly used node method, a simplified thermal dynamic model is proposed to capture temperature changes in networked pipelines. Quadratic, and polyhedral relaxations are then applied to convexify the original problem with quadratic equality, and bilinear constraints. Furthermore, an adaptive solution algorithm is developed to successively reduce the relaxation area based on sequential bound tightening, which improves solution optimality with desirable computational efficiency. The proposed method is verified on a distribution-level, and a transmission-level integrated electricity, and heat systems, compared to constant-flow-based solutions, and iterative algorithms.