Context : Sub-millimeter and Far-IR observations have shown the presence of a significant amount of warm ( few hundred K ) and dense ( n ( H _ { 2 } ) \geq 10 ^ { 4 } ~ { } { cm ^ { -3 } } ) gas in sources ranging from active star forming regions to the vicinity of the Galactic center . Since the main cooling lines of the gas phase are important tracers of the interstellar medium in Galactic and extragalactic sources , proper and detailed understanding of their emission , and the ambient conditions of the emitting gas , is necessary for a robust interpretation of the observations . Aims : With high resolution ( 7 ^ { \prime \prime } -9 ^ { \prime \prime } ) maps ( \sim 3 \times 3 pc ^ { 2 } ) of mid- J molecular lines we aim to probe the physical conditions and spatial distribution of the warm ( 50 to few hundred K ) and dense gas ( n ( H _ { 2 } ) > 10 ^ { 5 } ~ { } { cm ^ { -3 } } ) across the interface region of the nearly edge-on M17 SW nebula . Methods : We have used the dual color multiple pixel receiver CHAMP ^ { + } on APEX telescope to obtain a 5 ^ { \prime } .3 \times 4 ^ { \prime } .7 map of the J = 6 \rightarrow 5 and J = 7 \rightarrow 6 transitions of ^ { 12 } CO , the ^ { 13 } CO J = 6 \rightarrow 5 line , and the ^ { 3 } P _ { 2 } \rightarrow { { } ^ { 3 } P _ { 1 } } 370 \mu m fine-structure transition of [ C I ] in M17 SW. LTE and non-LTE radiative transfer models are used to constrain the ambient conditions . Results : The warm gas extends up to a distance of \sim 2.2 pc from the M17 SW ridge . The ^ { 13 } CO J = 6 \rightarrow 5 and [ C I ] 370 \mu m lines have a narrower spatial extent of about 1.3 pc along a strip line at P.A= 63 ^ { \circ } . The structure and distribution of the [ C I ] ^ { 3 } P _ { 2 } \rightarrow { { } ^ { 3 } P _ { 1 } } 370 \mu m map indicate that its emission arises from the interclump medium with densities of the order of 10 ^ { 3 } ~ { } { cm ^ { -3 } } . Conclusions : The warmest gas is located along the ridge of the cloud , close to the ionization front . An LTE approximation indicates that the excitation temperature of the embedded clumps goes up to \sim 120 K. The non-LTE model suggests that the kinetic temperature at four selected positions can not exceed 230 K in clumps of density n ( H _ { 2 } ) \sim 5 \times 10 ^ { 5 } ~ { } { cm ^ { -3 } } , and that the warm ( T _ { k } > 100 K ) and dense ( n ( H _ { 2 } ) \geq 10 ^ { 4 } ~ { } { cm ^ { -3 } } ) gas traced by the mid- J ^ { 12 } CO lines represent just about 2 % of the bulk of the molecular gas . The clump volume filling factor ranges between 0.04 and 0.11 at these positions .