Exergy (availability) is the amount of mechanical work that could be produced by reversible processes. This notion is revisited in the case when ambient temperature fluctuates. Simple examples are first considered, and then a theoretical approach is developed. It results that the most reliable way for combining entropy and total energy into an exergy function is a linear combination where entropy is multiplied by a constant temperature. It results that ambient air has non-zero exergy, but that exergy is surely conserved in ideal reversible processes. This approach is relevant for studying some recent problems in solar energy and building engineering.