The MHD equilibrium of thin, rotating plasma disks is considered. An axisymmetric steady state is assumed. A corotation lag is included, as is a nonzero toroidal field with Bϕ∝rBr. Rigorous expressions are obtained for a characteristic Alfv¿n Mach number and temperature, both of which involve vertical averages. If there is strict corotation, the temperature always diverges at large radii. If there is a corotation lag, the temperature need not diverge, and the magnetodisk solutions can extend to arbitrarily large radii. With weak additional assumptions, it is shown that MA<21/2 for a mainly poloidal field and MA<1 for a mainly toroidal field. For the Jovian magnetodisk, MA=0.8 from Voyager 1 inbound data, and the observation of a temperature nearly constant or slowly decreasing with r from 20 RJ to 80 RJ on the outbound pass implies a corotation lag there.