Haemoglobin (Hb)–O2 binding affinity typically decreases with increasing temperature, but several species of ectothermic and regionally endothermic fishes exhibit reduced Hb thermal sensitivity. Regionally endothermic sharks, including the common thresher shark (Alopias vulpinus) and lamnid sharks such as the shortfin mako shark (Isurus oxyrinchus), can maintain select tissues and organs warmer than ambient temperature by retaining metabolic heat with vascular heat exchangers. In the ectothermic bigeye thresher shark (Alopias superciliosus), diurnal movements above and below the thermocline subject the tissues, including the blood, to a wide range of operating temperatures. Therefore, blood–O2 transport must occur across internal temperature gradients in regionally endothermic species, and over the range of environmental temperatures encountered by the ectothermic bigeye thresher shark. While previous studies have shown temperature-independent Hb–O2 affinity in lamnid sharks, including shortfin mako, the Hb–O2 affinity of the common and bigeye thresher sharks is unknown. Therefore, we examined the effect of temperature on whole-blood Hb–O2 affinity in common thresher shark and bigeye thresher shark. For comparison, analyses were also conducted on the shortfin mako shark and two ectothermic species, blue shark (Prionace glauca) and spiny dogfish (Squalus acanthias). Blood–O2 binding affinity was temperature independent for common thresher shark and shortfin mako shark, which should prevent internal temperature gradients from negatively affecting blood–O2 transport. Blue shark and spiny dogfish blood–O2 affinity decreased with increasing temperature, as expected, but bigeye thresher shark blood exhibited both a reduced temperature dependence and a high Hb–O2 affinity, which likely prevents large changes in environment temperature and low environmental oxygen from affecting O2 uptake.