  The cosmic microwave background (CMB) temperature bispectrum is currently the
most precise tool for constraining primordial non-Gaussianity (NG). The Planck
temperature data tightly constrain the amplitude of local-type NG: $f_{\rm
NL}^{\rm loc} = 2.5 \pm 5.7$. Here, we compute previously-neglected foreground
biases in temperature-based $f_{\rm NL}^{\rm loc}$ measurements, due to the
integrated Sachs-Wolfe (ISW) effect, gravitational lensing, the thermal and
kinematic Sunyaev-Zel'dovich effects, and the cosmic infrared background. While
standard analyses already subtract a significant bias on $f_{\rm NL}^{\rm loc}$
due to the ISW-lensing bispectrum, many other secondary anisotropy terms are
present in the temperature bispectrum. We compute the dominant biases on
$f_{\rm NL}^{\rm loc}$ arising from these signals. Most of the biases are
non-blackbody, and are thus reduced by multifrequency component separation
methods; however, recent analyses have found that extragalactic foregrounds are
present at non-negligible levels in the Planck component-separated maps.
Moreover, the Planck FFP8 simulations do not include the foreground
correlations that generate these biases. We compute the biases for individual
frequencies; some are comparable to the statistical error bar on $f_{\rm
NL}^{\rm loc}$, even for the main CMB channels (100, 143, and 217 GHz). For
future experiments, they greatly exceed the statistical error (considering
temperature only). Alternatively, the foreground contributions can be
marginalized over, but this leads to a non-negligible increase in the error bar
on $f_{\rm NL}^{\rm loc}$. A full assessment will require calculations in
tandem with component separation, ideally using simulations. We also compute
these biases for equilateral and orthogonal NG, finding large effects for the
latter. We conclude that the search for primordial NG using Planck data may not
yet be over.
