Constraints on thermodynamic variables can be obtained using radar either by direct measurement or indirectly using retrievals. Radars can directly measure one component of target velocity, or more given additional radars or receivers, so long as there are detectable targets available. At close range, they can measure the refractive index of air near the surface given appropriate processing, providing a constraint on temperature and humidity. At far range, they remain blind to the lower troposphere, hence the push towards gap-filling radars.
Indirectly, using one or more radars, the time evolution of reflectivity and especially winds can be used to retrieve the forces shaping the storms, namely buoyancy and pressure gradients forces. From these, pressure and temperature gradients can be inferred, though the accuracy of such retrievals remains uncertain.
Unobtainable are average temperature and pressure profiles as well as humidity anywhere but near the surface and near a radar, except perhaps with dual-wavelength radars under very specific conditions.