  It is widely assumed that long-wavelength infrared (IR) emission from cold
dust (T~20-40K) 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 $\lambda\ga100$ \micron.
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 at $\lambda\ga100$ \micron, 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.
