Wear is a complex phenomenon that depends on the properties of materials and their surfaces, as well as the operating conditions and the surrounding atmosphere. At the micro-scale, abrasive wear occurs as material removal due to plastic deformation and fracture. In the present work, it is shown that fracture is stress-state-dependent and thus should be accounted for when modelling wear. For this reason, a three-dimensional finite element model has been adopted to simulate and study the main mechanisms that lead to wear of colliding asperities for a pair of metals. The model is also fully coupled with a non-linear thermal solver to account for thermal effects such as conversion of plastic work to heat as well as thermal expansion. It is shown that both the wear and flash temperature development are dependent on the stress triaxiality and the Lode parameter.