In Western countries, stroke is the third-most widespread cause of death. 80% of all strokes are ischemic and show a mortality rate of about 25%. Furthermore, 35-55% of affected patients retain a permanent disability. Therapeutic hypothermia (TH) could decrease inflammatory processes and the stroke-induced cerebral damage. Currently, the standard technique to induce TH is cooling of the whole body, which can cause several side effects. A novel cooling sheath uses intra-carotid blood cooling to induce local TH. Unfortunately, the control of the temporal and spatial cerebral temperature course requires invasive temperature measurements. Computational modeling could be used to predict the resulting temperature courses instead. In this work, a detailed 1D hemodynamics model of the cerebral arterial system was coupled with an energetic temperature model. For physiological conditions, 50% and 100% M1-stenoses, the temperatures in the supply area of the middle cerebral artery (MCA) and of the systemic body was analyzed. A 2K temperature decrease was reached within 10min of cooling for physiological conditions and 50% stenosis. For 100% stenosis, a significant lower cooling effect was observed, resulting in a maximum cerebral temperature decrease of 0.7K after 30min of cooling. A significant influence of collateral flow rates on the cooling effect was observed. However, regardless of the stenosis degree, the temperature decrease was strongest within the first 20min of cooling, which demonstrates the fast and effective impact of intra-carotid blood cooling.