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. With high resolution (7-9) maps (~3x3 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 M17 SW nebula. We have used the dual color multiple pixel receiver CHAMP+ on APEX telescope to obtain a 5.3x4.7 map of the J=6-5 and J=7-6 transitions of 12CO, the 13CO J=6-5 line, and the {^3P_2}-{^3P_1} 370 um fine-structure transition of [C I] in M17 SW. LTE and non-LTE radiative transfer models are used to constrain the ambient conditions. The warm gas extends up to a distance of ~2.2 pc from the M17 SW ridge. The 13CO J=6-5 and [C I] 370 um lines have a narrower spatial extent of about 1.3 pc along a strip line at P.A=63 deg. The structure and distribution of the [C I] {^3P_2}-{^3P_1} 370 um map indicate that its emission arises from the interclump medium with densities of the order of 10^3 cm^-3. 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 ~120 K. The non-LTE model suggests that the kinetic temperature at four selected positions cannot exceed 230 K in clumps of density n(H_2)~5x10^5 cm^-3, and that the warm T_k>100 K and dense (n(H_2)>10^4 cm^-3) gas traced by the mid-J 12CO 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.
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