We used the Atacama Pathfinder Experiment ( APEX ) 12 m telescope to observe the J _ { K _ { a } K _ { c } } = 3 _ { 03 } \rightarrow 2 _ { 02 } , 3 _ { 22 } \rightarrow 2 _ { 21 } , and 3 _ { 21 } \rightarrow 2 _ { 20 } transitions of para-H _ { 2 } CO at 218 GHz simultaneously to determine kinetic temperatures of the dense gas in the central molecular zone ( CMZ ) of our Galaxy . The map extends over approximately 40 { { } ^ { \prime } } \times 8 { { } ^ { \prime } } ( \sim 100 \times 20 pc ^ { 2 } ) along the Galactic plane with a linear resolution of 1.2 pc . The strongest of the three lines , the H _ { 2 } CO ( 3 _ { 03 } \rightarrow 2 _ { 02 } ) transition , is found to be widespread , and its emission shows a spatial distribution similar to ammonia . The relative abundance of para-H _ { 2 } CO is 0.5 - 1.2 \times 10 ^ { -9 } , which is consistent with results from lower frequency H _ { 2 } CO absorption lines . Derived gas kinetic temperatures for individual molecular clouds range from 50 K to values in excess of 100 K. While a systematic trend toward ( decreasing ) kinetic temperature versus ( increasing ) angular distance from the Galactic center ( GC ) is not found , the clouds with highest temperature ( T _ { kin } > 100 K ) are all located near the nucleus . For the molecular gas outside the dense clouds , the average kinetic temperature is 65 \pm 10 K. The high temperatures of molecular clouds on large scales in the GC region may be driven by turbulent energy dissipation and/or cosmic-rays instead of photons . Such a non-photon-driven thermal state of the molecular gas provides an excellent template for the more distant vigorous starbursts found in ultraluminous infrared galaxies ( ULIRGs ) .