  We investigate the bright CO fundamental emission in the central regions of
five Class 0 protostars using the JWST's Near-Infrared Spectrograph (NIRSpec)
and provide clues to what processes excite the gas. CO line emission images are
extracted for a forest of $\sim$150 ro-vibrational transitions from two
vibrational bands, $v=1-0$ and $v=2-1$. However, ${}^{13}$CO is not detected,
and thus we can only statistically constrain the ${}^{12}$CO optical depth.
Using noise measurements to determine upper limits to the ${}^{13}$CO emission,
the flux ratio of ${}^{12}$CO/${}^{13}$CO indicates that the ${}^{12}$CO
emission itself is not optically thick for ro-vibrational transitions with
upper state rotational quantum number $J_u \geq 15$. We construct population
diagrams to estimate the rotational temperature and number of molecules from
extinction-corrected CO line fluxes assuming CO emission is optically thin. Two
different temperature components are required for $v=1$ ($\sim600-1000$ K and
$\sim1500-3500$ K), while one hotter component is required for $v=2$
($\sim2000-6000$ K). The vibrational temperature is $\sim 900$ K among our
sources and shows no trend with luminosity. Using vibrational temperatures and
the inferred total amount of CO molecules for our sources, the total warm gas
mass correlates strongly with luminosity ranging from $\sim$0.1 $\rm M_{Earth}$
for the low-mass protostars to $\sim$1 M$_{\rm sun}$ for the high-mass
protostars. Interpreting the distribution of gas column densities and
temperatures depends on radiative and chemical processes affecting CO. The
presence of a $v=2$ population may indicate CO gas radiatively excited.
Selective UV photodissociation of CO isotopologues around our high-mass sources
may explain their depletion of ${}^{13}$CO.
