To address the issues of computational redundancy and communication burden in model predictive control (MPC) of indoor thermal environments, this study proposes an integral-type event-triggered control strategy. First, a simplified building resistant-capacitance (RC) thermal network model is established using an equivalent circuit method, incorporating the influence of adjacent thermal zones, and its accuracy is verified. Then an integral-type event-triggered mechanism (ITETM) based on state errors is introduced. Building on this mechanism, an integral-type event-triggered MPC method grounded in the RC thermal network model is formulated. Finally, the performance of the proposed control method is verified by co-simulation experiments using EnergyPlus and MATLAB. The results show that the proposed control strategy effectively reduces computational effort and communication frequency in the optimization process, while lowering building energy consumption and maintaining indoor thermal comfort.