To address the common neglect of electrolyzer heterogeneity and thermal effects in wind-solar hydrogen studies, a tri-objective energy management framework for a wind-photovoltaic-storage-hydrogen system with a heterogeneous electrolyzer cluster is proposed in this paper. The framework targets economic cost, specific hydrogen energy consumption, and thermal stability. Firstly, optimizable models are built for alkaline (ALK) electrolyzers and proton exchange membrane (PEM) electrolyzers. The models include minimum stable load, ramp-rate limits, efficiency characteristics, and thermoelectric coupling. They also describe the mapping from load ratio and stack temperature to hydrogen yield. A tri-objective optimization problem is formulated and solved using the improved non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ). The solver adopts feasibility-priority selection and repair operators to enhance constraint feasibility. Case studies show clear benefits over heterogeneous electrolyzer scheduling schemes that ignore energy consumption and thermal stability objectives. System profit increases by 4.48%. Specific hydrogen energy consumption decreases by 23%. Temperature deviation decreases by 9.46%. The results indicate that the proposed thermoelectric model and tri-objective strategy enable coordinated optimization of economy, efficiency, and thermal stability. They also reveal a cooperative operating pattern in which PEM units track fast fluctuations while ALK units provide efficient base operation.