The problem of local heating and temperature rise induced by dynamic crack growth in elastic-plastic solids is studied numerically. Heat generation caused by plastic work dissipation is estimated from crack-tip stress and deformation fields obtained separately by two of the authors. The temperature field in an Eulerian description is shown to be governed by a convection-dominated flow equation with a singular source term that is distributed over an irregular crack-tip region, the active plastic zone. The peak value and spatial distribution of the temperature increase are determined using two independent computer codes, which are developed by the authors based on an integral representation of the temperature field and on an upwind finite element formulation. The accuracy and reliability of the numerical methods and their solutions are studied carefully against exact, closed-form solutions for several specially designed boundary value problems. These methods are used to simulate dynamic fracture tests on AISI 4340 steel specimens, and the predicted temperature contours and maximum values are found to be in good agreement with those measured and estimated experimentally.