Some early-type galaxies show O VI emission, a tracer of gas at 105: 5 K, and a predicted product of gas cooling from the X-ray-emitting temperatures. We studied the spatial extent and velocity structure of this cooling gas by obtaining spectra of the O VI doublet in NGC 4636 and NGC 5846 with the Far Ultraviolet Spectroscopic Explorer. For NGC 4636, the central LWRS pointing shows that the O VI lines are double-peaked and symmetrical about the systemic velocity of the galaxy, with a separation of 210 km s(-1). An LWRS observation 3000 from the center failed to show additional O vi emission. For NGC 5846, three spectra were obtained with 400; 2000 apertures (MDRS) at the center and 400 to the east and west of the center. The O VI line flux seen in the previous LWRS is contained in the sum of the smaller apertures, with most of the flux in a single noncentral MDRS aperture, suggesting a size for the emission <= 0.5 kpc; the emission consists of a blue and red peak. For both galaxies, the O vi velocity structure is similar to that of the optical [N II] emission and is consistent with rotation. The compactness and velocity structure of the O VI emission rules out cooling flow models with broadly distributed mass dropout but is consistent with cooling flow models in which the cooling occurs primarily in the central region. The 104 K gas may be the end state of the O vi emitting gas.