We construct a new analytic phenomenological model for the extended circumgalactic material (CGM) of L * galaxies. Our model reproduces the OVII/OVIII absorption observations of the Milky Way (MW) and the OVI measurements reported by the COS-Halos and eCGM surveys. The warm/hot gas is in hydrostatic equilibrium in a MW gravitational potential, and we adopt a barotropic equation of state, resulting in a temperature variation as a function of radius. A pressure component with an adiabatic index of γ = 4/3 is included to approximate the effects of a magnetic field and cosmic rays. We introduce a metallicity gradient motivated by the enrichment of the inner CGM by the Galaxy. We then present our fiducial model for the corona, tuned to reproduce the observed OVI-OVIII column densities, and with a total mass of M CGM ≈ 5.5 × 10 10 M ⊙ inside r CGM ≈ 280 kpc. The gas densities in the CGM are low (n H = 10 −5 − 3 × 10 −4 cm −3 ) and its collisional ionization state is modified by the metagalactic radiation field (MGRF). We show that for OVI-bearing warm/hot gas with typical observed column densities N OVI ∼ 3 × 10 14 cm −2 at large ( 100 kpc) impact parameters from the central galaxies, the ratio of the cooling to dynamical times, t cool /t dyn , has a model-independent upper limit of ∼ 5. In our model, t cool /t dyn at large radii is ∼ 2 − 3. We present predictions for a wide range of future observations of the warm/hot CGM, from UV/X-ray absorption and emission spectroscopy, to dispersion measure (DM) and Sunyaev-Zeldovich CMB measurements.