The arterial supply to the eyes and brain of the common thresher shark, Alopias vulpinus, was examined and compared with that of five other lamniform shark species. Temperatures of the eyes and brain in two of these species were shown in previous studies to be higher than ambient. This was considered to be correlated with the presence of an orbital rete mirabile derived from the hyoidean efferent and pseudobranchial arteries. This study shows that the pseudobranchial artery forms a rete in only one of the two species previously shown to be warm, indicating that the brain of the other species is warmed by a non-retial vessel. This finding raises the possibility of brain and eye warming in Alopias vulpinus, which lacks an orbital rete mirabile.