The temperature (T) dependence of hole growth kinetics (HGK) data that span more than four decades of burn fluence are reported for aluminum-phthalocyanine tetrasulfonate (APT) in fresh and annealed hyperquenched glassy water (HGW) for temperatures between 5 and 20 K. The highly dispersive HGK data are modeled by using the "master" equation based on the two level system (TLS) model described in 2000 by Reinot and Small [J. Chem. Phys. 2000, 113, 10207]. We have demonstrated that thermal line broadening is not enough to account for temperature-dependent HGK for temperatures greater than 10 K. To overcome the discrepancy, the hole growth model must account for thermal hole filling (THF) processes. For the first time, the "master" equation used for HGK simulations is modified to take into account both the temperature dependence of the (single site) absorption spectrum and THF processes, effectively turning off those TLS which do not participate in the hole burning process at higher temperatures. A single set of parameters, some of which were determined directly from the hole spectra, was found to provide satisfactory fits to the HGK data for APT in fresh and annealed HGW for holes burned in the 679.7-676.9 nm range from the high to low energy sides of the Q(x) absorption band. Furthermore, we propose that HGK modeling at high burn fluences requires that the TLS model be further modified to take into account the existence of extrinsic multiple level systems.