We observed the cluster Abell 2218 (z=0.175), with ISOCAM on board the Infrared Space Observatory, using two filters with reference wavelengths of 6.7 and 14.3 microns. We detected 67 extragalactic mid-infrared sources. Using the ``GRASIL models of Silva et al. (1998) we have obtained acceptable and well constrained fits to the observed spectral energy distributions (SEDs) of 41 of these sources, for which additional optical/near-infrared magnitudes, and, in some cases, redshifts, were available. We have then determined the total infrared luminosities and star formation rates (SFRs) of these 41 sources, of which 27 are cluster members and 14 are field galaxies at a median redshift z~0.6. The SEDs of most of the ISOCAM cluster members are best fit by models with negligible star formation in the last ~1 Gyr. The 7 faintest cluster members have a slightly higher, but still very mild, star-formation activity. The ISOCAM-selected cluster galaxies appear to be an unbiased subsample of the overall cluster population. If A2218 is undergoing a merger, as suggested by some optical and X-ray analyses, then this merger does not seem to affect the mid-infrared properties of its galaxies. The SEDs of most ISOCAM-selected field sources are best fit by models with significant ongoing (and recent) star formation, resembling those of massive star-forming spirals or (post)starburst galaxies. Their median SFR is 22 solar masses per year. Eight of the 14 field sources are Luminous IR Galaxies. (Abridged)
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