Epilepsy is characterized by paroxysmal transient disturbances of the electrical activity of the brain. Symptoms are manifested as impairment of motor, sensory, or psychic function with or without loss of consciousness or convulsive seizures. This paper presents an initial post-operative heat transfer analysis of surgery performed on a 41 year-old man with medically intractable Epilepsy. The surgery involved tumor removal and the resection of adjacent epileptogenic tissue. Electrocorticography was performed before resection. Cold saline was applied to the resulting interictal spike foci resulting in transient, complete cessation of spiking. A transient one dimensional semi-infinite finite element model of the surface of the brain was developed to simulate the surgery. An approximate temperature distribution of the perfused brain was developed by applying the bioheat equation. The model quantifies the surface heat flux reached in achieving seizure cessation to within an order of magnitude. Rat models have previously shown that the brain surface temperature range to rapidly terminate epileptogenic activity is 20-24°C. The developed model predicts that a constant heat flux of approximately -13,000W/m2, applied at the surface of the human brain, would achieve a surface temperature in this range in approximately 3 seconds. A parametric study was subsequently performed to characterize the effects of brain metabolism and brain blood perfusion as a function of the determined heat flux. The results of these findings can be used as a first approximation in defining the specifications of a cooling device to suppress seizures in human models.