  We aim to better understand the heating of the gas by observing the prominent
gas cooling line [CII] at 158um in the low-metallicity environment of the Local
Group spiral galaxy M33 at scales of 280pc. In particular, we aim at describing
the variation of the photoelectric heating efficiency with galactic
environment. In this unbiased study, we used ISO/LWS [CII] observations along
the major axis of M33, in combination with Herschel PACS and SPIRE continuum
maps, IRAM 30m CO 2-1 and VLA HI data to study the variation of velocity
integrated intensities. The ratio of [CII] emission over the far-infrared
continuum is used as a proxy for the heating efficiency, and models of
photon-dominated regions are used to study the local physical densities, FUV
radiation fields, and average column densities of the molecular clouds. The
heating efficiency stays constant at 0.8% in the inner 4.5kpc radius of the
galaxy where it starts to increase to reach values of ~3% in the outskirts at
about 6kpc radial distance. The rise of efficiency is explained in the
framework of PDR models by lowered volume densities and FUV fields, for optical
extinctions of only a few magnitudes at constant metallicity. In view of the
significant fraction of HI emission stemming from PDRs, and for typical
pressures found in the Galactic cold neutral medium (CNM) traced by HI
emission, the CNM contributes ~15% to the observed [CII] emission in the inner
2kpc radius of M33. The CNM contribution remains largely undetermined in the
south, while positions between 2 and 7.3kpc radial distance in the north of M33
show a contribution of ~40%+-20%.
