When relatively cold fluid is injected to hot host rock featured with fractures, the fluid-rock temperature difference induces cooling of the self-propping fractures and could cause the failure of the asperity. Although fracture sustainability has been extensively studied, little research has focused on thermal effects on asperity failure. A finite-element analysis is conducted to investigate the effect of fluid-rock temperature differences on the asperity failure. In the analysis, rock mechanical properties are coupled with the temperature and stress states of the host rock. The thermally-induced tensile cracks initiate at the junction of asperity and rock matrix and also start at rim of contact tip at higher temperature difference. When the temperature difference is high enough to propagate tensile cracks, two groups of tensile cracks would coalesce and lead to asperity failure. The critical threshold to initiate two groups of tensile cracks is identified in this study. This asperity failure could also result in the closure of fractures and change the fracture network distribution in the rock. Further, the comparison with fracture wall with no asperity addresses the effect of the asperity on the growth pattern of secondary thermal cracks.