We present CI 3P1-3P0 spectra at four spiral arm positions and the nuclei of the nearby galaxies M83 and M51 obtained at the JCMT. This data is complemented with maps of CO 1-0, 2-1, and 3-2, and ISO/LWS far-infrared data of CII (158 micron), OI (63 micron), and NII (122 micron) allowing for the investigation of a complete set of all major gas cooling lines. From the intensity of the NII line, we estimate that between 15% and 30% of the observed CII emission originate from the dense ionized phase of the ISM. The analysis indicates that emission from the diffuse ionized medium is negligible. In combination with the FIR dust continuum, we find gas heating efficiencies below ~0.21% in the nuclei, and between 0.25 and 0.36% at the outer positions. Comparison with models of photon-dominated regions (PDRs) of Kaufman et al. (1999) with the standard ratios OI(63)/CII_PDR and (OI(63)+CII_PDR) vs. TIR, the total infrared intensity, yields two solutions. The physically most plausible solution exhibits slightly lower densities and higher FUV fields than found when using a full set of line ratios, CII_PDR/CI(1-0), CI(1-0)/CO(3-2), CO(3-2)/CO(1-0), CII/CO(3-2), and, OI(63)/CII_PDR. The best fits to the latter ratios yield densities of 10^4 cm^-3 and FUV fields of ~G_0=20-30 times the average interstellar field without much variation. At the outer positions, the observed total infrared intensities are in perfect agreement with the derived best fitting FUV intensities. The ratio of the two intensities lies at 4-5 at the nuclei, indicating the presence of other mechanisms heating the dust.
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