We have used ISO to observe at 12$μ$m seven E+A galaxies plus an additional emission line galaxy, all in the Coma cluster. E+A galaxies lacking narrow emission lines have 2.2$μ$m to 12$μ$m flux density ratios or limits similar to old stellar populations (typical of early-type galaxies). Only galaxies with emission lines have enhanced 12$μ$m flux density. Excess 12$μ$m emission is therefore correlated with the presence of on-going star formation or an active galactic nucleus (AGN). By comparing the current star formation rates with previous rates estimated from the Balmer absorption features, we divide the galaxies into two groups: those for which star formation has declined significantly following a dramatic peak $\sim$ 1 Gyr ago; and those with a significant level of ongoing star formation or/and an AGN. There is no strong difference in the spatial distribution on the sky between these two groups. However, the first group has systemic velocities above the mean cluster value and the second group below that value. This suggests that the two groups differ kinematically. Based on surveys of the Coma cluster in the radio, the IRAS sources, and galaxies detected in H$α$ emission, we sum the far infrared luminosity function of galaxies in the cluster. We find that star formation in late type galaxies is probably the dominant component of the Coma cluster far infrared luminosity. The presence of significant emission from intracluster dust is not yet firmly established. The member galaxies also account for most of the far infrared output from nearby rich clusters in general.

AAS Latex, accepted for publication in ApJ