Early-type galaxies often contain a hot X-ray-emitting interstellar medium [(3-8) x 10(6) K] with an apparent radiative cooling time much less than a Hubble time. If unopposed by a heating mechanism, the gas will radiatively cool to temperatures less than or similar to 10(4) K at a rate proportional to L-X/T-X, typically 0.03-1 M-circle dot yr(-1). We can test whether gas is cooling through the 3 x 10(5) K range by observing the O VI doublet, whose luminosity is proportional to the cooling rate. Here we report on a study of an unbiased sample of 24 galaxies, obtaining Far Ultraviolet Spectroscopic Explorer spectra to complement the X-ray data of ROSAT and Chandra. The O VI line emission was detected in about 40% of the galaxies and at a luminosity level similar to the prediction from the cooling flow model. There is a correlation between. M-O (VI) and M-X, although there is significant dispersion about the relationship, where the O VI is brighter or dimmer than expected by a factor of 3 or more. If the cooling flow picture is to be retained, then this dispersion requires that cooling flows be time-dependent, as might occur by the activity of an AGN. However, of detected objects, those with the highest or lowest values of. M-O (VI)/M-X are not systematically hot or cool, as one might predict from AGN heating.