We consider the radiative cooling of warm (T greater-than-or-equal-to
100 K), fully molecular astrophysical gas by rotational and vibrationa
l transitions of the molecules H2O, CO, and H-2. Using an escape proba
bility method to solve for the molecular level populations, we have ob
tained the cooling rate for each molecule as a function of temperature
, density, and an optical depth parameter. A four-parameter expression
proves useful in fitting the run of cooling rate with density for any
fixed values of the temperature and optical depth parameter. We ident
ify the various cooling mechanisms which are dominant in different reg
ions of the astrophysically relevant parameter space. Given the assump
tion that water is very abundant in warm regions of the interstellar m
edium, H2O rotational transitions are found to dominate the cooling of
warm interstellar gas over a wide portion of the parameter space cons
idered. While chemical models for the interstellar medium make the str
ong prediction that water will be produced copiously at temperatures a
bove a few hundred degrees, our assumption of a high water abundance h
as yet to be tested observationally. The Infrared Space Observatory an
d the Submillimeter Wave Astronomy Satellite will prove ideal instrume
nts for testing whether water is indeed an important coolant of inters
tellar and circumstellar gas.