  The uncertainty surrounding the nature of the heating mechanism for the dust
that emits at mid- to far-IR (MFIR) wavelengths in active galaxies limits our
understanding of the links between active galactic nuclei (AGN) and galaxy
evolution, as well as our ability to interpret the prodigious infrared and
sub-mm emission of some of the most distant galaxies in the Universe. Here we
report deep Spitzer observations of a complete sample of powerful, intermediate
redshift (0.05 < z < 0.7) radio galaxies and quasars. We show that AGN power,
as traced by [OIII]5007 emission, is strongly correlated with both the mid-IR
(24 micron) and the far-IR (70 micron) luminosities, however, with increased
scatter in the 70 micron correlation. A major cause of this increased scatter
is a group of objects that falls above the main correlation and displays
evidence for prodigious recent star formation activity at optical wavelengths,
along with relatively cool MFIR colours. These results provide evidence that
illumination by the AGN is the primary heating mechanism for the dust emitting
at both 24 and 70 microns, with starbursts dominating the heating of the cool
dust in only 20 -- 30% of objects. This implies that powerful AGN are not
always accompanied by the type of luminous starbursts that are characteristic
of the peak of activity in major gas-rich mergers.
