  The background photon temperature $\bar T$ is one of the fundamental
cosmological parameters. Despite its significance, $\bar T$ has never been
allowed to vary in the data analysis, owing to the precise measurement of the
comic microwave background (CMB) temperature by COBE FIRAS. However, even in
future CMB experiments, $\bar T$ will remain unknown due to the unknown
monopole contribution $\Theta_0$ at our position to the observed
(angle-averaged) temperature $\langle T\rangle^{\rm obs}$. By fixing $\bar
T\equiv\langle T\rangle^{\rm obs}$, the standard analysis underestimates the
error bars on cosmological parameters, and the best-fit parameters obtained in
the analysis are biased in proportion to the unknown amplitude of $\Theta_0$.
Using the Fisher formalism, we find that these systematic errors are smaller
than the error bars from the $Planck$ satellite. However, with $\bar
T\equiv\langle T\rangle^{\rm obs}$, these systematic errors will always be
present and irreducible, and future cosmological surveys might misinterpret the
measurements.
