We present optical spectra for a sample of 563 high-latitude IRAS sources selected from the Point Source Catalog to have relatively warm 25 to 60 micron colours. We have shown this selection criterion to be an efficient indicator for finding Seyfert galaxies. Plots of the optical spectra are shown and the fluxes of the strongest emission lines in these spectra are tabulated. After excluding 128 sources which are clearly galactic foreground objects, we obtained spectroscopic information for 358 extragalactic objects. Emission-line ratios have been used to classify these objects, resulting in 80 Seyfert 1, 141 Seyfert 2 and 133 HII-type objects. In comparison with samples of active nuclei selected in other ways, about 50% of known Seyfert nuclei are included by our colour criteria. This fraction is larger for high luminosities, reaching 80% for quasar luminosities. For lower-luminosity objects, contamination by the host galaxies becomes important and the sample becomes seriously incomplete. It should be moderately complete and representative for core luminosities greater than 10^23.5^W/Hz at 12m. Finally, the infrared luminosity function for each type of object is derived; the shapes for Seyfert 1 and 2 nuclei are identical, with a type 2/type 1 space-density ratio of 3.0. Our census is consistent with an obscuration scheme for producing both types of object from a single parent population, though the origin of excess cool IR radiation Irom many Seyferts is still unclear. We note the appearance of an apparent type II supernova in IRAS 0225-103 observed in 1985 September. Its spectrum suggests that it was observed between 1 and 2 months after maximum, perhaps in a "plateau" phase.