Temperature-dependent sex determination (TSD) has evolved independently in at least two lineages of viviparous Australian scincid lizards, but its adaptive significance remains unclear. We studied a montane lizard species (Eulamprus heatwolei) with TSD. Our data suggest that mothers can modify the body sizes of their offspring by selecting specific thermal regimes during pregnancy (mothers with higher and more stable temperatures produced smaller offspring), but cannot influence sons versus daughters differentially in this way. A field mark-recapture study shows that optimal offspring size differs between the sexes: larger body size at birth enhanced the survival of sons but reduced the survival of daughters. Thus, a pregnant female can optimize the fitness of either her sons or her daughters (via yolk allocation and thermoregulation), but cannot simultaneously optimize both. One evolutionary solution to reduce this fitness cost is to modify the sex-determining mechanism so that a single litter consists entirely of either sons or daughters; TSD provides such a mechanism. Previous work has implicated a sex difference in optimal offspring size as a selective force for TSD in turtles. Hence, opposing fitness determinants of sons and daughters may have favored evolutionary transitions from genetic sex determination to TSD in both oviparous turtles and viviparous lizards.