The purpose of this paper is to describe a method for determining a cooling template for galaxies, using nearby galaxies, and applicable to future observations of distant galaxies. We observed two starburst galaxies (NGC 253 and Henize 2-10) with the Caltech Submillimeter Observatory in the rotational lines of carbon monoxide 12CO(J=3-2), (J=6-5) and (J=7-6) for both, and also 12CO(J=4-3) and 13CO(J=3-2) for Henize 2-10 and in the 3P2-3P1 fine-structure transitions of atomic carbon [CI] at 809GHz for NGC 253. Some of these observations have been made previously, but the present multitransition study (including data found in the literature) is the most complete to date for the two galaxies. From these observations, we have derived the properties of the warm and dense molecular gas in the galaxy nuclei. We used an LTE analysis and an LVG radiative transfer model to determine physical conditions of the interstellar medium in both sources and predicted integrated line properties of all CO transitions up to 12CO(15-14). We found the observations to be in good agreement with a medium characterized by Tk≃50-100K, (12CO)/(13CO)≃30, n(H2)>104cm–3 and N(12CO)=3.5±1x1018cm–2 for Henize 2-10 and characterized by Tk≃70-150K, (12CO)/(13CO)≃40, n(H2)>104cm–3 and N(12CO)=1.5±0.5x1019cm2 for NGC 253. A PDR model has also been used and here the data are well fitted (within 20%) by a model cloud with a gas density of n(H)=8.0±1x105cm3 and an incident FUV flux of χ≃20000 for Henize 2-10. For NGC 253, we deduced n(H)=3.0±0.5x105cm–3 and χ≃20000 for the modelled cloud. The physical properties of warm gas and CO cooling curves of the target galaxies are compared with those measured for the nucleus of the Milky Way and the Cloverleaf QSO. The gas properties and CO cooling curve are similar for the two starburst galaxies and the Cloverleaf QSO while the Milky Way nucleus exhibits lower excitation molecular gas.