These features, long called the UIRs or unidentified infrared bands, can be seen in this ISO spectrum of the colliding starburst system NGC 6090. The IRAS survey showed that far-IR emission is ubiquitous among spiral and irregular galaxies, even some for which optical data suggested a very modest dust content. Some fraction of this emission is powered by young stars, making far-IR emission a very tempting indicator of star formation if we can understand it properly. For thermal emission, dust grains are heated by absorption of starlight, which operates most effectively in the blue and UV as the wavelength comes closer to the characteristic grain size. In fact, this cold dust is dominant by mass over the much brighter dust seen out to 100 microns.
Global considerations are more interesting.
In most galaxies, the SFR changes slowly enough conmpared to the lifetimes of hot stars that you'd expect similar correlations with indicators of stars having lifetimes up to a Gyr. There remains controversy as to whether young stars are the dominant heating mechanism, or whether there is a significant contribution from older, cooler stars. The existence of very cool components in some galaxies' far-IR and mm spectra indicates that such dust is common. In calculating the dust mass, it becomes important that the grains are much smaller than the wavelengths of peak emission. For whole galaxies, values of the exponent near -1 fit well.