Thermal runaway is a ductile localization mechanism that has been linked to deep-focus earthquakes and pseudotachylyte formation. In this study, we investigate the dynamics of this process using one-dimensional, numerical models of simple shear deformation. The models employ a visco-elastic rheology where viscous creep is accommodated with a composite rheology encompassing diffusion and dislocation creep as well as low-temperature plasticity. To solve the nonlinear system of differential equations governing this rheology, we utilize the pseudo-transient iterative method in combination with a viscosity regularization to avoid resolution dependencies. To determine the impact of different model parameters on the occurrence of thermal runaway, we perform a parameter sensitivity study consisting of 6000 numerical experiments. We observe two distinct behaviors, namely a stable regime, characterized by transient shear zone formation accompanied by a moderate (100 - 300 Kelvin) temperature increase, and a thermal runaway regime, characterized by strong localization, rapid slip and a temperature surge of thousands of Kelvin. Nondimensional scaling analysis allows us to determine two dimensionless groups that predict model behavior. The ratio t_r/t_d represents the competition between heat generation from stress relaxation and heat loss due to thermal diffusion while the ratio U_el/U_th compares the stored elastic energy to thermal energy in the system. Thermal runaway occurs if t_r/t_d is small and U_el/U_th is large. Our results demonstrate that thermal runaway is a viable mechanism driving fast slip events that are in line with deep-focus earthquakes and pseudotachylyte formation at conditions resembling cores of subducting slabs.