The time-of-flight technique was used to study hole transport in largely amorphous thin films (similar to 1 mu m) of chloroaluminum phthalocyanine (ClAlPc) that were obtained with various amounts of structural organization by vacuum subliming the molecular material on substrates maintained at various temperatures T-s, ranging from -40 to 140 degrees C. The first paper of a series of two reports the drift mobility measurements performed between 333 and 213 K. In that range of measurement temperatures, T-m, the thermally activated charge transport is discussed within the framework of the disorder formalism due to Bassler and co-workers. The expected field and temperature dependence of mobility as well as the convoluted temperature dependence of the field dependencies agrees well with the predictions of the formalism throughout the structural variation employed. The width of the distribution of site energies, sigma, is found to decrease from 110 to 76 meV over the rise in substrate temperature, while the positional disorder parameter, Sigma, also decreases from a value of 3.00 to a minimum value of 1.87. This is in accordance with the expected increase in film organization, as previously verified by transmission electron microscopy. The use of a single material with different amounts of disorder then allows comparison with further predicted trends that are otherwise experimentally inaccessible. The room-temperature mobility increases by an order of magnitude from similar to 10(-5) to 10(-4) cm(2)/(V s) over the same T-s rise, saturating at the higher substrate temperatures. The mobility at zero-field, infinite temperature, and no disorder, mu(00), is also found to increase by an order of magnitude over the same rise in substrate temperatures and is seen as a direct indicator of enhanced wave function overlap in less disorganized samples on heated substrates. Unprecedented reversals in the trends of time-of-flight results obtained at T-m < 213 K for the group of chloroaluminum, chlorogallium, and chloroindium phthalocyanines are reported in the companion paper.