Absorption and fluorescence spectral properties of J-aggregates of core-tetrasubstituted perylene bisimide (PBI) dyes have been investigated in the temperature range from 300 to 5 K. A special feature of the present PBI J-aggregates is that, in contrast to classical J-aggregates like that of pseudoisocyanine (PIC), the chromophores are held together not only by van-der-Waals interactions but also by hydrogen bonds. The temperature dependence of the spectral band widths and the Stokes shift for PBI 1 aggregates are compared with those for 3,3'-bis-(3-sulfopropyl)-5,5'-dichloro-9-ethylthiacarbocyanine (THIATS) J-aggregates, which have been studied in detail previously (J. Phys. Chem. B 2001, 105, 4636-4646). The assemblies of PBI 1 possess very broad absorption bands compared to those of THIATS, even at low temperature (5 times broader). We interpret this observation as an indication for a very large level of disorder in the case of PBI I assemblies. Possible sources of disorder in aggregates of PBI 1 are discussed. Despite large quantitative differences, both aggregates show qualitatively the same temperature dependence of the Stokes shift calculated in units of fluorescence bandwidth. The observed temperature dependences are discussed in terms of exciton thermal population of different states of disordered aggregates. Unexpectedly low thermal activation energy of exciton migration is observed for PBI 1 aggregates.