The invention is a method of monitoring the temperature to which an object has been exposed. The invention comprises combining a Time-Temperature Indicator (TTI) with an electronic monitoring device to determine whether the temperature to which the object has been exposed may have exceeded a predetermined threshold. The TTI device can be used to make a rapid initial determination as to the acceptability of the temperature history. The temperature history stored in the electronic monitoring device can be retrieved if visual inspection of the TTI indicates that the temperature history may possibly have exceeded the predetermined threshold. As a result, rejection of goods based on inaccurate TTI readings can be reduced or prevented, and the amount of time needed to retrieve data from an electronic monitoring device can be limited to only those circumstances where the initial visualization of the TTI indicates the possibility of an unacceptable temperature history.