We construct an analytic phenomenological model for extended warm/hot gaseous coronae of $L_*$ galaxies. We consider UV OVI COS-Halos absorption line data in combination with Milky Way X-ray OVII and OVIII absorption and emission. We fit these data with a single model representing the COS-Halos galaxies and a Galactic corona. Our model is multi-phased, with hot and warm gas components, each with a (turbulent) log-normal distribution of temperatures and densities. The hot gas, traced by the X-ray absorption and emission, is in hydrostatic equilibrium in a Milky Way gravitational potential. The median temperature of the hot gas is $1.5 times 10^6$~K and the mean hydrogen density is $sim 5 times 10^{-5}~{rm cm^{-3}}$. The warm component as traced by the OVI, is gas that has cooled out of the high density tail of the hot component. The total warm/hot gas mass is high and is $1.2 times 10^{11}~{rm M_{odot}}$. The gas metallicity we require to reproduce the oxygen ion column densities is $0.5$ solar. The warm OVI component has a short cooling time ($sim 2 times 10^8$ years), as hinted by observations. The hot component, however, is $sim 80%$ of the total gas mass and is relatively long-lived, with $t_{cool} sim 7 times 10^{9}$ years. Our model supports suggestions that hot galactic coronae can contain significant amounts of gas. These reservoirs may enable galaxies to continue forming stars steadily for long periods of time and account for missing baryons in galaxies in the local universe.
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