Shear localization plays a major role during geodynamic processes and in particular during the formation of shear zones on all geological scales. However, the thermo-mechanical mechanisms responsible for shear localization are still debated and incompletely understood. Shear localization in a homogenous ductile material requires a softening mechanism and we consider here thermal softening. Thermal softening is the result of the conversion of mechanical work into heat (i.e. shear heating) and of the temperature dependence of rock viscosities. We present results of dimensional analysis and scaling for shear zones caused by thermal softening in a temperature-sensitive power-law viscous fluid. The scaling is performed in combination with 1-D numerical simulations to determine dimensionless parameters which can predict the evolution of temperature and of shear zone thickness. The 1-D results are based on a simple shear model configuration. We compare the 1-D results with 2-D and also 3-D results of numerical simulations for a pure shear configuration where shear zones are initiated by a small circular thermal perturbation. We further investigate thermal softening in a viscoelastic (Maxwell) fluid to quantify the evolution of elastic strain energy and thermal energy during shear localization. We show that elasticity can have a significant impact on strain localization. Finally, we present 2-D numerical simulations of lithospheric shortening which show the formation of orogenic wedges. The shear zones controlling the wedge formation are due to thermal softening. Shear zones due to thermal softening have a physics-controlled thickness which is independent on the numerical resolution. Therefore, we can quantify the evolution of stress, strain and temperature inside these shear zones and compare numerical results with independent estimates from field observations and laboratory derived flow laws.