A thermographic phosphor's decay time distribution over its temperature-sensitive range was retrieved with the Maximum Entropy Method (MEM). A decay time distribution consists of a range of decay times, each with an associated weighting for the decay time component's prevalence in the analyzed decay curve. With the MEM, significant decay time contributions of a decay curve have high weighting and are therefore found as peaks in the decay time distribution, where the width and peak value are correlated with the relative weight of the decay time components. These peaks in the decay time distribution give increased insight into a phosphor's lifetime behavior, which often cannot accurately be represented by a single or even two decay time components. The changes in the location of peaks in the decay time distribution with temperature can be used for thermometry, and this method has the benefit of being less sensitive to the multi-exponentiality of phosphor decay than mono-exponential decay time fitting. The method also resolves the underlying decay components with no assumptions of the number of significant decay time components. Initially, when the decay time distribution of Mg4FGeO6:Mn was captured, the collected decay included decaying luminescence from the alumina oxide tube in the tube furnace. Therefore, a second calibration was performed where the luminescence from the alumina oxide tube was minimized. These two calibration datasets were used to demonstrate that the MEM could characterize decays from two separate sources simultaneously.