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Using a large-scale natural experiment in staggered billing dates for energy use in Germany and a unique billing dataset for multi-apartment buildings, this paper shows that the month of billing is a significant determinant of heat energy consumption. A large set of residential buildings demand significantly more heat energy annually, when the bill is issued during off-winter months. The paper finds evidence for salience cycles of heating bills that last up to 4 months, likely because consumer attention to heat energy costs is short-lived and absent during months when heating is off. Importantly, this phenomena is pervasive enough to be detectable even in aggregated building-level consumption data. Results suggest that the mere knowledge of costs is not sufficient and that the response to billing information also hinges on its time-varying salience. These findings underscore the importance of understanding the dynamic and heterogeneous nature of cost salience in the design of effective billing for energy conservation.