Temperature management of the food supply-chain is important for ensuring compliance and the quality of perishable products like vaccines and fish. While conventional strategies have relied on using monitors attached to packaging containers, self-powered time-temperature monitoring is attractive because the technology can be embedded with passive RFID tags and can be integrated with every food or medical package. In this paper we propose a self-powered sensor that can monitor the time-temperature information without the need for any external powering. The sensor exploits the physics of Fowler-Nordheim (FN) tunneling where electrons are thermally excited and are continuously integrated on a floating-gate. The steady-state FN integrator's response depends on the temperature and corresponds to a temporal curve that is unique to a specific ambient temperature. Deviation from the set ambient temperature results in the deviation from its reference response curve hence can be captured by the sensor. Measured results from sensors prototyped in a 0.5 μm CMOS process show a temperature sensitivity of 1.5mV/°C over a monitoring duration of 100 hours.