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Aims. We present an overview of a high-mass star formation region through the major (sub-)mm, and far-infrared cooling lines to gain insight into the physical conditions and the energy budget of the molecular cloud. Methods. We used the KOSMA 3m telescope to map the core (10' x 14') of the Galactic star-forming region DR21/DR21 (OH) in the Cygnus X region in the two fine structure lines of atomic carbon (Ci (3)P(1)- (3)P(0) and (3)P(2)- (3)P(1)), in four mid-J transitions of CO and (13)CO, and in CS J = 7- 6. These observations were combined with FCRAO J = 1-0 observations of (13)CO and C(18)O. Five positions, including DR21, DR21 (OH), and DR21 FIR1, were observed with the ISO/LWS grating spectrometer in the [O I] 63 and 145 mu m lines, the [C II] 158 mu m line, and four high-J CO lines. We discuss the intensities and line ratios at these positions and apply the local thermal equilibrium (LTE) and non-LTE analysis methods in order to derive physical parameters such as mass, density and temperature. The CO line emission was modeled up to J = 20. Results. From non-LTE modeling of the low- to high-J CO lines, we identify two gas components, a cold one at temperatures of T(kin) similar to 30- 40 K and one with T(kin) similar to 80-150K at a local clump density of about n(H(2)) similar to 10(4)-10(6) cm(-3). While the cold quiescent component is massive, typically containing more than 94% of the mass, the warm, dense, and turbulent gas is dominated by mid-and high-J CO line emission and its large line widths. The medium must be clumpy with a volume-filling of a few percent. The CO lines are found to be important in cooling the cold molecular gas, e. g. at DR21 (OH). Near the outflow of the UV-heated source DR21, the gas cooling is dominated by line emission of atomic oxygen and of CO. Atomic and ionised carbon play a minor role

The cooling of atomic and molecular gas in DR21