Hydrogen production by water electrolysis is an effective way to smooth the fluctuation of renewable energy sources. However, the power response ability of alkaline water electrolyzers is greatly influenced by the stack temperature. The long response time lowers the flexibility of hydrogen energy storage. To address the problem, an equivalent circuit model considering thermal characteristics is proposed to depict the relationship between the electrolyzer power and stack temperature. Based on the model, a control strategy aiming at the efficient cold start of electrolyzer is proposed. The electrolyzer is heating by the maximum input power in the first stage and after the stack reaches the temperature corresponding to the maximum power, the electrolyzer will operate in the most efficient mode. The effectiveness of the proposed model and control strategy are verified by the experimental results.