The tendency of asphaltenes for aggregation followed by precipitation and deposition plays a crucial role in the petroleum industry since these processes present severe problems during the production, recovery, and processing of crude oils and fossil hydrocarbon feedstocks. The dynamics of oil asphaltene aggregates dissolved in chloroform at different concentrations varied in a wide range that was investigated at temperatures from 0 to 55 °C using the Pulsed-Field Gradient NMR technique. The components attributed to nanoaggregates and macroaggregates were successfully resolved, which allowed us to measure their diffusion coefficients. The diffusion coefficients for all types of aggregates grow as the asphaltene concentration decreases, whereas the partial weight of the aggregates increases with the increase of asphaltene concentration. The difference in diffusion behavior of the aggregates of different types was registered when passing the critical concentration range 10–20 g/L. The nano- and macroaggregates behave independently when the asphaltene concentration is higher than 20 g/L (concentrated regime), while below 20 g/L (semidiluted regime) the components related to the different types of aggregates cannot be properly resolved. It was found that regardless of the asphaltene concentration, the diffusion coefficients for nano- and macroaggregates demonstrate similar temperature behavior giving the straight lines in the Arrhenius coordinates which change their slopes when passing the temperature range 20–30 °C. The phenomenon evidences the thermally induced cleavage of noncovalent bonds with subsequent rearrangement of asphaltene aggregates that is observed for all concentration regimes covering the existence of asphaltene aggregates of all types. The data obtained are well consistent with the modern concept of asphaltene aggregate structure and fairly agree with the data obtained earlier. We believe these results will contribute essentially to a better understanding of the fundamental behavior of asphaltenes and their aggregates, providing a deep insight into aggregate transformation triggered by the temperature.