  It is widely assumed that long-wavelength infrared (IR) emission from cold
dust (T~20-40 K) is a reliable tracer of star formation even in the presence of
a bright active galactic nucleus (AGN). Based on radiative transfer (RT) models
of clumpy AGN tori, hot dust emission from the torus contributes negligibly to
the galaxy spectral energy distribution (SED) at $\lambda>60\,\mu$m. However,
these models do not include AGN heating of host-galaxy-scale diffuse dust,
which may have far-IR (FIR) colors comparable to cold diffuse dust heated by
stars. To quantify the contribution of AGN heating to host-galaxy-scale cold
dust emission, we perform dust RT calculations on a simulated galaxy merger
both including and excluding the bright AGN that it hosts. By differencing the
SEDs yielded by RT calculations with and without AGN that are otherwise
identical, we quantify the FIR cold dust emission arising solely from
re-processed AGN photons. In extreme cases, AGN-heated host-galaxy-scale dust
can increase galaxy-integrated FIR flux densities by factors of 2-4; star
formation rates calculated from the FIR luminosity assuming no AGN contribution
can overestimate the true value by comparable factors. Because the FIR colors
of such systems are similar to those of purely star-forming galaxies and redder
than torus models, broadband SED decomposition may be insufficient for
disentangling the contributions of stars and heavily dust-enshrouded AGN in the
most IR-luminous galaxies. We demonstrate how kpc-scale resolved observations
can be used to identify deeply dust-enshrouded AGN with cool FIR colors when
spectroscopic and/or X-ray detection methods are unavailable.
