The increasingly wide application of technologies such as combined heat and power (CHP) systems and micro energy management systems has enhanced the coupling of various types of energy. In this paper, a generalized Nash game model is built in this paper to simulate the multi-round auction in combined heat and power market (CHPM). In this model, the consumer demand curves are deduced from the partial derivatives of their payoff functions, and the thermal comfort of the consumers is considered in their payoff functions. The integrated energy suppliers (IES) compete with each other in the CHPM. The generalized Nash game model is applied to describe their rational economic behavior. First, the existence and uniqueness of the generalized Nash equilibrium is proven in detail. Subsequently, a distributed algorithm based on the augmented Lagrangian approach is designed to solve this generalized Nash game model. Through the distributed algorithm, the participants can protect their privacy without revealing their generation parameters or energy consumption schedule to other participants. Finally, by simulating the multi-round auction, it was found that the proposed method has faster convergence than standard Lagrangian approaches.