Smalleye Pacific opah and swordfish can conserve metabolic heat and maintain specific body regions warmer than ambient water temperature (i.e. regional heterothermy). Consequently, blood O2 uptake at the gills occurs at the environmental temperature at which the individual is found, but O2 offloading will occur at different temperatures in different tissues. While several regionally heterothermic fishes (e.g. billfishes, tunas and sharks) show a reduced temperature effect on haemoglobin (Hb)–O2 affinity, the temperature dependence of Hb–O2 affinity in opah and swordfish is unknown. We hypothesized that the Hb of opah and swordfish would also show a reduced temperature dependence. Opah whole-blood–O2 affinity exhibited a reverse temperature dependence above 50% Hb–O2 saturation (10–20°C, pH 7.2–8.0), while the temperature dependence of swordfish blood–O2 affinity (10–25°C) was saturation and pH dependent, becoming temperature independent below 50% Hb–O2 saturation and pH 7.4. Experiments on stripped haemolysates showed that adding ATP ([ATP]/[Hb]=30) decreased the temperature sensitivity of Hb–O2 affinity, changing the overall oxygenation enthalpy (ΔH′) values of opah (10–20°C) and swordfish (10–25°C) Hbs at pH 7.4 from −15 and −42 kJ mol−1 O2, respectively, to +84 and −9 kJ mol−1 O2. Swordfish blood–O2 affinity was high compared with that of other large, pelagic, marine teleosts, which may be the result of unusually low ATP/Hb levels, but might also enable swordfish to forage in the potentially low-oxygenated water of the upper reaches of the oxygen minimum layer. The existence of Hbs with reduced temperature sensitivity in regionally heterothermic fishes may prevent marked changes in Hb–O2 affinity between the cold and warm tissues.