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Recent research has shown the potential of Model-based Reinforcement Learning (MBRL) to enhance energy efficiency of Heating, Ventilation, and Air Conditioning (HVAC) systems. However, existing methods rely on black-box thermal dynamics models and stochastic optimizers, lacking reliability guarantees and posing risks to occupant health. In this work, we overcome the reliability bottleneck by redesigning HVAC controllers using decision trees extracted from existing thermal dynamics models and historical data. Our decision tree-based policies are deterministic, verifiable, interpretable, and more energy-efficient than current MBRL methods. First, we introduce a novel verification criterion for RL agents in HVAC control based on domain knowledge. Second, we develop a policy extraction procedure that produces a verifiable decision tree policy. We found that the high dimensionality of the thermal dynamics model input hinders the efficiency of policy extraction. To tackle the dimensionality challenge, we leverage importance sampling conditioned on historical data distributions, significantly improving policy extraction efficiency. Lastly, we present an offline verification algorithm that guarantees the reliability of a control policy. Extensive experiments show that our method saves 68.4% more energy and increases human comfort gain by 14.8% compared to the state-of-the-art method, in addition to an 1127x reduction in computation overhead. Our code and data are available at https://github.com/ryeii/Veri_HVAC