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The [CII] $158\,\mu\mathrm{m}$ fine-structure line is one of the dominantcoolants of the neutral interstellar medium. It is hence one of the brightestfar-infrared emission lines and can be observed not only in star-formingregions throughout the Galaxy, but also in the diffuse interstellar medium andin distant galaxies. [CII] line emission has been suggested to be a powerfultracer of star-formation. We aim to understand the origin of [CII] emission andits relation to other tracers of interstellar gas and dust. This includes astudy of the heating efficiency of interstellar gas as traced by the [CII] lineto test models of gas heating. We make use of a one-square-degree map ofvelocity-resolved [CII] line emission towards the Orion Nebula complex,including M43 and NGC 1977. The [CII] intensity is tightly correlated with PAHemission in the IRAC $8\,\mu\mathrm{m}$ band and far-infrared emission fromwarm dust. The correlation between [CII] and CO(2-1) is affected by thedetailed geometry of the region. We find particularly low [CII]-over-FIRintensity ratios towards large columns of (warm and cold) dust, which suggestthe interpretation of the "[CII] deficit" in terms of a "FIR excess". A slightdecrease in the FIR line-over-continuum intensity ratio can be attributed to adecreased heating efficiency of the gas. We find that, at the mapped spatialscales, predictions of the star-formation rate from [CII] emissionunderestimate the star-formation rate calculated from YSO counts in the OrionNebula complex by an order of magnitude. [CII] emission from the Orion Nebulacomplex arises dominantly in the cloud surfaces, many viewed in edge-ongeometry. [CII] emission from extended faint cloud surfaces may contributesignificantly to the total [CII] emission on galactic scales.

[CII] $158\,\mu\mathrm{m}$ line emission from Orion A. I. A template for extragalactic studies?