This paper investigates temperature rise distribution near a crack tip of CT specimens of a mild steel due to plastic work under intermediate loading rate for the purpose of considering the criterion for crack instability under arbitrary loading rate. The dynamic thermal elastoplastic FEM analysis shows good agreement with experimental temperature rise distributions by using a thermo viewer. The calculation results of yield stress in the process zone in the vicinity of a crack tip is fairly constant because of opposed effects of strain rate and temperature on yield stress. Moreover yield stress in the process zone increases with increasing loading rates up to a certain rate due to the increase in strain rate, however, the increase in loading rates over the certain value leads to decrease in yield stress which is caused by local heating near a crack tip due to plastic work because there is not enough time to dissipate heat. From the above information, the criterion of fracture initiation under arbitrary loading rate is conducted. Experimental Kc values of HT-50 TMCP steel with various loading rates support quantitatively the criteria.