This paper presents a model of a cold storage warehouse combined with PV generation in a smart grid setting. We formulate an optimization problem that maximizes profits of sold PV energy minus the cost of electricity withdrawn from the grid under constraints dictated by the temperature dynamics. We focus on the influence of different electricity tariff structures on the optimal cooling schedule that results from the optimization. The results show that the various tariff structures lead to markedly different optimal cooling trajectories, that can be understood in terms of the trade-offs between thermal leakage to the environment, time dependent PV revenues and prices for consuming electricity. The value of the optimized energy management vs uncontrolled cooling was found to be largest for the case where electricity prices were low during PV generation. This type of responsive demand can therefore facilitate the efficient integration of renewable energy sources in the power system.