A temperature-time integrating indicator for determining the safe limit of torage of a food product or other material which is subject to deterioration due to temperature and length of storage. In its preferred form the temperature-time integrating indicator comprises a transparent polymeric film package containing a warning message enclosed in the package together with an aqueous solution of a redox dye, e.g., sodium anthraquinone beta-sulfonate. The dye is in its reduced state, which is dark red and obscures the warning message. The rate of permeation of oxygen into the package is a function of the temperature at which the package is exposed to the atmospheric environment. When sufficient time has elapsed at temperatures which may vary, the due becomes oxidized, turning colorless and revealing the warning message. The effects of temperature and time on the migration of oxygen through the polymeric film followed by reaction of the oxygen with the redox dye in the solution are integrated. This is related to product deterioration in storage, since the rate of this deterioration also depends on the temperature history and the time of storage. The use or disposal of stored foods and the like may be scheduled in accordance with warnings provided by the temperature-time integrating indicators.