In earlier studies on damage to model DNA systems caused by low-energy electrons, we considered electrons that attach either to cytosine's lowest pi*-orbital or to a P=O pi*-orbital of a phosphate unit. We examined a range of electron kinetic energies (E) (e.g., representative of the Heisenberg width of the lowest pi*-resonance state of cytosine), and we determined how the rates of cleavage of the sugar-phosphate C-O a-bond depend on E and on the solvation environment. In the P=O attachment study, we showed that electrons of ca. 1.0 eV could attach to form a pi*-anion, which then could break either a 3' or 5' O-C sigma-bond connecting the phosphate to either of two attached sugar groups. In the present study, we extend the base-attachment aspect of our work and consider electrons having kinetic energies below 1 eV attaching to thymine's lowest pi*-orbital, again examining the energy and solvation dependence of the resulting rates of C-O sigma-bond cleavage.