Interplay of CMB Temperature, Space Curvature, and Expansion Rate
  Parameters
  The cosmic microwave background (CMB) temperature, $T$, surely the most
precisely measured cosmological parameter, has been inferred from {\it local}
measurements of the blackbody spectrum to an exquisite precision of 1 part in
$\sim 4700$. On the other hand, current precision allows inference of other
basic cosmological parameters at the $\sim 1\%$ level from CMB power spectra,
galaxy correlation and lensing, luminosity distance measurements of supernovae,
as well as other cosmological probes. A basic consistency check of the standard
cosmological model is an independent inference of $T$ at recombination. In this
work we first use the recent Planck data, supplemented by either the first year
data release of the dark energy survey (DES), baryon acoustic oscillations
(BAO) data, and the Pantheon SNIa catalog, to extract $T$ at the $\sim 1\%$
precision level. We then explore correlations between $T$, the Hubble
parameter, $H_{0}$, and the global spatial curvature parameter, $\Omega_{k}$.
Our parameter estimation indicates that imposing the local constraint from the
SH0ES experiment on $H_{0}$ results in significant statistical preference for
departure at recombination from the locally inferred $T$. However, only
moderate evidence is found in this analysis for tension between local and
cosmological estimates of $T$, if the local constraint on $H_{0}$ is relaxed.
All other dataset combinations that include the CMB with either BAO, SNIa, or
both, disfavor the addition of a new free temperature parameter even in the
presence of the local constraint on $H_{0}$. Analysis limited to the Planck
dataset suggests the temperature at recombination was higher than expected at
recombination at the $\gtrsim 95\%$ confidence level if space is globally flat.
