We present results of a detailed study of a sample of nearby galaxies, based on previous work, that aims to connect both local / resolved and integrated galaxy properties related to dust, ISM and star-formation. Dust temperatures are derived for all galaxies, knowing the dust masses previously derived through a self-consistent method and considering a modified black-body function (MBB) for the cold dust emission SED fit. The range and temperature values for the sample are found to be consistent with values from other similar studies. Further, the dust emissivity index (β) is calculated and its evolution with the temperature is shown, Moreover, it is investigated if it can be predicted from or if it scales with any local / integrated dust/ISM or galaxy properties. We analyse established and new relations between the dust temperature, dust emissivity index and the surface densities of dust, star-formation and stellar mass, and other related local and integrated quantities. We also show how the diffuse dust distribution in the stellar disc compares with the extent of star-formation distribution and the stellar continuum emission one, and their evolution with stellar mass.