In this paper, we are at first demonstrating 3D-SPRITE which has been shown to be successful for studying short relaxation time systems and which is free from distortions due to susceptibility variations for coals. The results obtained were discussed in relation to the three-dimensional distribution of mobile components for two kinds of coal. At the same time, inversion recovery preparation experiments, for example, T-1 mapping and T-2* mapping based on SPRITE methods are presented in order to clarify the chemical heterogeneity of coals. Also, we have carried out the first systematic in-situ variable-temperature NMR microimaging study of coals between 25 and 600 degreesC with our newly developed high-temperature microimaging probe and systems in order to clarify the behavior of mobile components at high temperatures in heterogeneous coal specimens. Both the mechanism of softening and melting process for coals and the coal mapping for the softening and melting properties using in-situ imaging experiments which are based on the local information are proposed.