Acute ischemic stroke is a major health problem with a high mortality rate and a high risk for permanent disabilities. Selective brain hypothermia has the neuroprotective potential to possibly lower cerebral harm. A recently developed catheter system enables to combine endovascular blood cooling and thrombectomy using the same endovascular access. By using the penumbral perfusion via leptomeningeal collaterals, the catheter aims at enabling a cold reperfusion, which mitigates the risk of a reperfusion injury. However, cerebral circulation is highly patient-specific and can vary greatly. Since direct measurement of remaining perfusion and temperature decrease induced by the catheter is not possible without additional harm to the patient, computational modeling provides an alternative to gain knowledge about resulting cerebral temperature decrease. In this work, we present a brain temperature model with a realistic division into gray and white matter and consideration of spatially resolved perfusion. Furthermore, it includes detailed anatomy of cerebral circulation with possibility of personalizing on base of real patient anatomy. For evaluation of catheter performance in terms of cold reperfusion and to analyze its general performance, we calculated the decrease in brain temperature in case of a large vessel occlusion in the middle cerebral artery (MCA) for different scenarios of cerebral arterial anatomy. Congenital arterial variations in the circle of Willis had a distinct influence on the cooling effect and the resulting spatial temperature distribution before vessel recanalization. Independent of the branching configurations, the model predicted a cold reperfusion due to a strong temperature decrease after recanalization (1.4-2.2 C after 25 min of cooling, recanalization after 20 min of cooling). Our model illustrates the effectiveness of endovascular cooling in combination with mechanical thrombectomy and its results serve as an adequate substitute for temperature measurement in a clinical setting in the absence of direct intraparenchymal temperature probes.