When the four-wheel independent drive electric vehicle (4WIDEV) operates continuously under high-load conditions, the temperature of the insulated-gate bipolar transistor (IGBT) module will rapidly rise, making it susceptible to triggering the predesigned thermal protection strategy (TPS). This will cause a sudden drop in corresponding motor output torque, leading to a reduction in vehicle power performance and potentially causing instability. To solve this problem, a robust model predictive control (MPC)-based vehicle stability control strategy for 4WIDEV considering IGBT thermal effect is proposed. Firstly, a control-oriented IGBT thermal model is established to represent the electro-thermal effects of the IGBT module. A test bench is built to verify the IGBT thermal model and obtain the boundaries of uncertain parameters in this model. Secondly, considering uncertain parameters with known boundaries, a linear parameter varying (LPV) discrete system model is established, composed of the IGBT thermal model and vehicle dynamics model. Then a robust MPC-based vehicle stability controller is proposed. IGBT temperature constraints are constructed to keep the temperature below the threshold, considering parameter uncertainties. Additionally, three constraints are established to satisfy the stability conditions and robustness requirements of the 4WIDEV. Finally, the proposed control strategy is verified by hardware-in-the-loop (HIL) experiments. The simulation results under scenarios where IGBT temperatures are approaching the threshold demonstrate that the proposed strategy improves tracking performance for velocity and yaw rate by 54.7% and 87.2%, respectively, compared to the existing method, while effectively avoiding triggering the TPS.