No Redshift Evolution of Dust Temperatures from $0 < z < 2$
  Some recent literature has claimed there to be an evolution in galaxies' dust
temperatures towards warmer (or colder) spectral energy distributions (SEDs)
between low and high redshift. These conclusions are driven by both theoretical
models and empirical measurement. Such claims sometimes contradict one another
and are prone to biases in samples or SED fitting techniques. What has made
direct comparisons difficult is that there is no uniform approach to fitting
galaxies' infrared/millimeter SEDs. Here we aim to standardize the measurement
of galaxies' dust temperatures with a python-based SED fitting procedure,
MCIRSED. We draw on reference datasets observed by IRAS, Herschel, and Scuba-2
to test for redshift evolution out to $z\sim2$. We anchor our work to the
L$_{IR}$-$\lambda_{peak}$ plane, where there is an empirically observed
anti-correlation between IR luminosity and rest-frame peak wavelength (an
observational proxy for luminosity-weighted dust temperature) such that
$\lambda_{peak}=\lambda_{t}({L_{IR}}/{L_{t}})^{\eta}$ where
$\eta=-0.09\pm0.01$, L$_{t}=10^{12}$ L$_{\odot}$, and $\lambda_{t}=92\pm2\mu$m.
We find no evidence for redshift evolution of galaxies' temperatures, or
$\lambda_{peak}$, at fixed L$_{IR}$ from $0<z<2$ with >99.99% confidence. Our
finding does not preclude evolution in dust temperatures at fixed stellar mass,
which is expected from a non-evolving L$_{IR}$-$\lambda_{peak}$ relation and a
strongly evolving SFR-M$_\star$ relation. The breadth of dust temperatures at a
given L$_{IR}$ is likely driven by variation in galaxies' dust geometries and
sizes and does not evolve. Testing for L$_{IR}$-$\lambda_{peak}$ evolution
toward higher redshift ($z\sim5-6$) requires better sampling of galaxies' dust
SEDs near their peaks (observed $\sim$200-600$\mu$m) with $<$1 mJy sensitivity.
This poses a significant challenge to current instrumentation.
