  We analyse a comprehensive set of MIR/FIR observations of Stephan's Quintet
(SQ), taken with the Spitzer Space Observatory. Our study reveals the presence
of a luminous (L_{IR}\approx 4.6x10^43 erg/s) and extended component of
infrared dust emission, not connected with the main bodies of the galaxies, but
roughly coincident with the X-ray halo of the group. We fitted the inferred
dust emission spectral energy distribution of this extended source and the
other main infrared emission components of SQ, including the intergalactic
shock, to elucidate the mechanisms powering the dust and PAH emission, taking
into account collisional heating by the plasma and heating through UV and
optical photons. Combining the inferred direct and dust-processed UV emission
to estimate the star formation rate (SFR) for each source we obtain a total SFR
for SQ of 7.5 M(sun)/yr, similar to that expected for non-interacting galaxies
with stellar mass comparable to the SQ galaxies. Although star formation in SQ
is mainly occurring at, or external to the periphery of the galaxies, the
relation of SFR per unit physical area to gas column density for the brightest
sources is similar to that seen for star-formation regions in galactic disks.
We also show that available sources of dust in the group halo can provide
enough dust to produce up to L_{IR}\approx 10^42 erg/s powered by collisional
heating. Though a minority of the total infrared emission (which we infer to
trace distributed star-formation), this is several times higher than the X-ray
luminosity of the halo, so could indicate an important cooling mechanism for
the hot IGM and account for the overall correspondence between FIR and X-ray
emission.
