The [CII] $158,mumathrm{m}$ fine-structure line is one of the dominant coolants of the neutral interstellar medium. It is hence one of the brightest far-infrared emission lines and can be observed not only in star-forming regions throughout the Galaxy, but also in the diffuse interstellar medium and in distant galaxies. [CII] line emission has been suggested to be a powerful tracer of star-formation. We aim to understand the origin of [CII] emission and its relation to other tracers of interstellar gas and dust. This includes a study of the heating efficiency of interstellar gas as traced by the [CII] line to test models of gas heating. We make use of a one-square-degree map of velocity-resolved [CII] line emission towards the Orion Nebula complex, including M43 and NGC 1977. The [CII] intensity is tightly correlated with PAH emission in the IRAC $8,mumathrm{m}$ band and far-infrared emission from warm dust. The correlation between [CII] and CO(2-1) is affected by the detailed geometry of the region. We find particularly low [CII]-over-FIR intensity ratios towards large columns of (warm and cold) dust, which suggest the interpretation of the [CII] deficit in terms of a FIR excess. A slight decrease in the FIR line-over-continuum intensity ratio can be attributed to a decreased heating efficiency of the gas. We find that, at the mapped spatial scales, predictions of the star-formation rate from [CII] emission underestimate the star-formation rate calculated from YSO counts in the Orion Nebula complex by an order of magnitude. [CII] emission from the Orion Nebula complex arises dominantly in the cloud surfaces, many viewed in edge-on geometry. [CII] emission from extended faint cloud surfaces may contribute significantly to the total [CII] emission on galactic scales.
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