A recently developed quantum mechanical approach devoted to the study of unstable species in solution was applied to isomeric radicals resulting from the addition of hydrogen atoms to thymine. The computational protocol includes either post-Hartree-Fock or density functional electronic computations, together with simulation of the solvent by a polarizable continuum, and averaging of spectroscopic properties over thr most important vibrational motions. Concerning electronic computations, hybrid Hartree-Fock/density functional models (here B3LYP) provide reliable results both for structural and spectroscopic parameters. In contrast. pure Hartree-Fock or low-order perturbative many-body approaches (here MP2) stand against considerable difficulties in the treatment of open-shell systems. Starting from B3LYP computations, vibrational averaging by the out of plane motions and, to a lower extent, consideration of solvent effects lend to remarkable agreement between the computed hyperfine coupling constants and experimental data.