The physical structure of a protoplanetary disk determines the mechanisms responsible for the disk's dynamical evolution as well as how the earliest phases of planetary accumulation proceeded. Thermal and density profiles control the extent to which processes such as self-gravitational forces, convective instability, and magnetic fields contribute to the dynamical evolution of the disk. Thermal profiles also affect the chemical composition of the grain aggregates that eventually formed planetesimals through their control of the condensation and sublimation of iron, silicate, and ice grains. A two-dimensional radiative hydrodynamics code has been used to compute a number of quasi-static models of protoplanetary disks. Variations explored by the models include changes in the disk mass, stellar mass, disk mass accretion rate, initial adiabat, radial density profile, energy source, and dust grain opacity. The models represent temporal " snapshots" that can be used to infer the evolution of disks as, e.g., the disk mass or disk mass accretion rates decrease. A general property of low-mass (～ 0.02 solar mass) disks being heated by mass accretion from the cloud envelope at ～10~(-6) to 10~(-5) solar mass yr~(-1) is a relatively hot (midplane temperature T_m > 1200 K) inner region surrounded by a much cooler (T_m ～100 K) outer disk. Such a thermal profile naturally leads to the formation of rocky inner planets and icy outer planets, with the ice condensation point never falling closer than about 3 AU from the protostar—giant planets must form outside this radius. Midplane temperatures greater than 1200 K are consistent with the depletions of moderately volatile elements observed in inner solar system bodies. Disk temperatures drop sufficiently with vertical height or radial position, or with decreased disk mass or disk mass accretion rates, to permit the plausible incorporation of both ～1200 K and less than 700 K components in chondritic meteorites. Surface densities of low-mass disks appear to be inadequate for the disk to evolve through gravitational torques, and the models tend to be largely stable with respect to convection, which could otherwise lead to turbulence and significant viscous torques. Thermal ionization of K and Na may allow the generation of significant magnetic fields near the midplane in the inner disk, while cosmic rays and short-lived nuclides ionize the outer disk, perhaps eliminating the possibility of a field-free gap between these two regions and allowing continued magnetically driven inflow of disk mass to the protostar.
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