The water skinks Eulamprus tympanum and Eulamprus heatwolei show thermally induced sex determination where elevated temperatures give rise to male offspring. Paradoxically, Eulamprus species reproduce in temperatures of 12-15 °C making them outliers when compared with reptiles that use temperature as a cue for sex determination. Moreover, these two species are among the very few viviparous reptiles reported to have thermally induced sex determination. Thus, we tested whether these skinks possess undetected sex chromosomes with thermal override. We produced transcriptome and genome data for E. heatwolei. We found that E. heatwolei presents XY chromosomes that include 14 gametologs with regulatory functions. The Y chromosomal region is 79-116 Myr old and shared between water and spotted skinks. Our work provides clear evidence that climate could be useful to predict the type of sex determination systems in reptiles and it also indicates that viviparity is strictly associated with sex chromosomes.