The temperature (T) dependence of hole growth kinetics (HGK) data that span more than four decades of burn fluence are reported for aluminum-phthalocyanine tetrasulphonate in fresh and annealed hyperquenched glassy water for temperatures between 5 and 20 K. The highly dispersive HGK data are modeled using the “master” equation based on the two level system (TLS) model described in [J. Chem. Phys., 2000, 113, 10207]. This study shows that the temperature dependence of the hole burning rate becomes significantly less important when the T-induced absorption rate is taken into account for temperatures below 10 K. However, as the temperature approaches 10 K and above, it is found that the T-induced absorption rate is not enough to account for the T-dependence of the hole growth rate at longer burning times. We argue that the additional slowdown of the hole growth rate as temperature increases is associated with thermal hole filling (THF), a process which prevents faster burning chromophores from contributing to the persistent spectral hole. We account for the THF process by modifying the “master” equation so as to eliminate those chromophores in the TLS model that do not participate in the persistent non-photochemical hole burning process at temperatures higher than 10 K. Furthermore, to account for discrepancies in the HGK model at high burn fluence, we propose that it is necessary to modify the TLS model to take into account the existence of extrinsic multiple level systems.