This paper highlights some caveats in using composite analyses to form physical hypotheses on the associations between environmental variables. This is illustrated using a specific example, namely the apparent links between heat waves (HWs) and sea surface temperatures (SSTs). In this case study, a composite analysis is performed to show the large-scale and regional SST conditions observed during summer HWs in Perth, southwest Australia. Composite results initially point to the importance of the subtropical South Indian Ocean, where physically coherent SST dipole anomalies appear to form a necessary condition for HWs to develop across southwest Australia. However, sensitivity tests based on pattern correlation analyses indicate that the vast majority of days when the identified SST pattern appears are overwhelmingly not associated with observed HWs, which suggests that this is definitely not a sufficient condition for HW development. Very similar findings are obtained from the analyses of 15 coupled climate model simulations. The results presented here have pertinent implications and applications for other climate case studies, and highlight the importance of applying comprehensive statistical approaches before making physical inferences on apparent climate associations.