Slow structural relaxations can complicate the interpretation of thermodynamic measurements on glass-forming liquids. Here we demonstrate using model calculations that structural recovery can lead to an apparent frequency-dependent heat capacity in ac calorimetry experiments. The model is shown to describe the complex heat capacity data reported in the literature for glycerol and poly(vinyl acetate). Importantly, the model does not invoke a complex heat capacity; rather, only static heat capacities are used. The analysis further suggests that ac calorimetry should provide a powerful way of testing models of structural recovery.