J-aggregates of the dye THIATS (triethylammonium salt of 3,3 ' -bis-[3-sulfopropyl]-5,5 ' -dichloro-9-ethylthia-carbocyanine) with a two-component Davydov splitting of the exciton band were investigated in the temperature range from 5 to 130 K and at room temperature. A wide set of excitonic and optical characteristics (absorption line broadening, fluorescence line broadening, Stokes shift, coherence length, exciton migration rate, and wavelength dependence of the fluorescence decay time) of the same J-aggregates is presented. The exciton migration rate was found to be the most temperature sensitive property. The temperature dependence of a whole set of exciton properties reveals two critical temperatures: 30 and 70 K. The observed phenomena are described qualitatively as an interplay of static and dynamic disorder effects. At low temperature (T < 20 K) static disorder is the main factor which limits the coherence length and exciton-exciton annihilation rate and determines the absorption width. An intraband, subnanosecond exciton relaxation toward the lower energy states is observed. Below 20 K only a limited number of exciton states of the molecular ensemble are reached by the exciton during downhill relaxation. While the temperature increases from 30 to 70 K, a wider set of states becomes accessible for the exciton during its relaxation. The "internal" structure of the exciton band becomes blurred by homogeneous broadening and the coherence length decreases. Very fast exciton wave packet motion occurs over 10(6)-10(7) molecules. At temperatures higher than 80 K, we suggest dynamical processes to play the most important role. The Stokes shift becomes temperature independent. Exciton migration starts to be strongly blocked by scattering on optical phonons. The effective, long distance exciton migration in THIATS J-aggregates as well as peculiarities of the Stokes shift and line broadening temperature dependence allow us to conclude that no exciton self-trapping process occurs at temperatures higher than 20 K.