According to the concept of the "minimal boundary curve for endothermy", mammals and birds with a basal metabolic rate (BMR) that falls below the curve are obligate heterotherms and must enter torpor. We examined the reliability of the boundary curve (on a double log plot transformed to a line) for predicting torpor as a function of body mass and BMR for birds and several groups of mammals. The boundary line correctly predicted heterothermy in 87.5% of marsupials (n = 64), 94% of bats (n = 85) and 82.3% of rodents (n = 157). Our analysis shows that the boundary line is not a reliable predictor for use of torpor. A discriminate analysis using body mass and BMR had a similar predictive power as the boundary line. However, there are sufficient exceptions to both methods of analysis to suggest that the relationship between body mass, BMR and heterothermy is not a causal one. Some homeothermic birds (e.g. silvereyes) and rodents (e.g. hopping mice) fall below the boundary line, and there are many examples of heterothermic species that fall above the boundary line. For marsupials and bats, but not for rodents, there was a highly significant phylogenetic pattern for heterothermy, suggesting that taxonomic affiliation is the biggest determinant of heterothermy for these mammalian groups. For rodents, heterothermic species had lower BMRs than homeothermic species. Low BMR and use of torpor both contribute to reducing energy expenditure and both physiological traits appear to be a response to the same selective pressure of fluctuating food supply, increasing fitness in endothermic species that are constrained by limited energy availability. Both the minimal boundary line and discriminate analysis were of little value for predicting the use of daily torpor or hibernation in heterotherms, presumably as both daily torpor and hibernation are precisely controlled processes, not an inability to thermoregulate.