  The Galactic center is the closest region in which we can study star
formation under extreme physical conditions like those in high-redshift
galaxies. We measure the temperature of the dense gas in the central molecular
zone (CMZ) and examine what drives it. We mapped the inner 300 pc of the CMZ in
the temperature-sensitive J = 3-2 para-formaldehyde (p-H$_2$CO) transitions. We
used the $3_{2,1} - 2_{2,0} / 3_{0,3} - 2_{0,2}$ line ratio to determine the
gas temperature in $n \sim 10^4 - 10^5 $cm$^{-3}$ gas. We have produced
temperature maps and cubes with 30" and 1 km/s resolution and published all
data in FITS form. Dense gas temperatures in the Galactic center range from ~60
K to > 100 K in selected regions. The highest gas temperatures T_G > 100 K are
observed around the Sgr B2 cores, in the extended Sgr B2 cloud, the 20 km/s and
50 km/s clouds, and in "The Brick" (G0.253+0.016). We infer an upper limit on
the cosmic ray ionization rate ${\zeta}_{CR} < 10^{-14}$ 1/s. The dense
molecular gas temperature of the region around our Galactic center is similar
to values found in the central regions of other galaxies, in particular
starburst systems. The gas temperature is uniformly higher than the dust
temperature, confirming that dust is a coolant in the dense gas. Turbulent
heating can readily explain the observed temperatures given the observed line
widths. Cosmic rays cannot explain the observed variation in gas temperatures,
so CMZ dense gas temperatures are not dominated by cosmic ray heating. The gas
temperatures previously observed to be high in the inner ~75 pc are confirmed
to be high in the entire CMZ.
