  We searched for thermal gyro-synchrotron radio emission from a sample of five
radio-loud stars whose X-ray coronae contain a hot ($T_e>10^7$ K) thermal
component. We used the JVLA to measure Stokes I and V/I spectral energy
distributions (SEDs) over the frequency range 15--45 GHz, determining the
best-fitting model parameters using power-law and thermal gyro-synchrotron
emission models. The SEDs of the three chromospherically active binaries
(Algol, UX Arietis, HR 1099) were well-fit by a power-law gyro-synchrotron
model, with no evidence for a thermal component. However, the SEDs of the two
weak-lined T Tauri stars (V410 Tau, HD 283572) had a circularly polarized
enhancement above 30 GHz that was inconsistent with a pure power-law
distribution. These spectra were well-fit by summing the emission from an
extended coronal volume of power-law gyro-synchrotron emission and a smaller
region with thermal plasma and a much stronger magnetic field emitting thermal
gyro-synchrotron radiation. We used Bayesian inference to estimate the physical
plasma parameters of the emission regions (characteristic size, electron
density, temperature, power-law index, and magnetic field strength and
direction) using independently measured radio sizes, X-ray luminosities, and
magnetic field strengths as priors, where available. The derived parameters
were well-constrained but somewhat degenerate. The power-law and thermal
volumes in the pre-main-sequence stars are probably not co-spatial, and we
speculate they may arise from two distinct regions: a tangled-field
magnetosphere where reconnection occurs and a recently discovered axisymmetric
toroidal magnetic field, respectively.
