Several previous reports, often from studies utilising heavily instrumented animals, have indicated that for teleosts, the increase in cardiac output ( ) during exercise is mainly the result of an increase in cardiac stroke volume (V_S) rather than in heart rate (f_H). More recently, this contention has been questioned following studies on animals carrying less instrumentation, though the debate continues. In an attempt to shed more light on the situation, we examined the heart rates and oxygen consumption rates ( ; normalised to a mass of 1 kg, given as ) of six Murray cod (Maccullochella peelii peelii; kg) equipped with implanted f_H and body temperature data loggers. Data were determined during exposure to varying temperatures and swimming speeds to encompass the majority of the biological scope of this species. An increase in body temperature (T_b) from 14°C to 29°C resulted in linear increases in (26.67–41.78 μmol min⁻¹ kg⁻¹) and f_H (22.3–60.8 beats min⁻¹) during routine exercise but a decrease in the oxygen pulse (the amount of oxygen extracted per heartbeat; 1.28–0.74 μmol beat⁻¹ kg⁻¹). During maximum exercise, the factorial increase in was calculated to be 3.7 at all temperatures and was the result of temperature‐independent 2.2‐ and 1.7‐fold increases in f_H and oxygen pulse, respectively. The constant factorial increases in f_H and oxygen pulse suggest that the cardiovascular variables of the Murray cod have temperature‐independent maximum gains that contribute to maximal oxygen transport during exercise. At the expense of a larger factorial aerobic scope at an optimal temperature, as has been reported for species of salmon and trout, it is possible that the Murray cod has evolved a lower, but temperature‐independent, factorial aerobic scope as an adaptation to the largely fluctuating and unpredictable thermal climate of southeastern Australia.