Surface heat flow offers a unique perspective from which to image the Earth. However, reliable data is difficult to collect and this has necessitated a reliance on industrial datasets collected during exploration for mineral and petroleum resources. Resulting data-quality issues have limited the ability of previous studies to map the information contained in the data into robust model inferences. Here I employ a Bayesian statistical framework to address these issues under the auspices of re-appraising the Australian crustal heat flow field. The physical basis for conductive heat transport informs the framework, while a priori knowledge of system parameters constrains inference in data-poor areas. These features combine to produce predictions of Australian surface heat flow, including a quantification of prediction uncertainty. The significance of these outcomes is that they provide the means to calculate the extent with which a given Earth model is consistent with available geothermal data. In doing so, I establish the basis for future data integration projects to build detailed models of Australian crustal structure and composition, and to better constrain the Australian lithospheric heat budget.