The shared tectonic history of southwestern Australia and East Antarctica facilitates the exchange of geological insights between the regions. In this study, we present coupled susceptibility and density models obtained through the joint inversion of magnetic and gravity data. By assuming a common geological source for both signals, our coupling method minimizes misfits and variation in information, thereby enhancing the correlation between susceptibility and density. The resulting anomalies demonstrate structural continuity between the continents, aligning closely with major shear zones and seismic reflectors. Combining these results with machine learning, geochemical, and petrophysical databases, we predict a high-resolution ($10$ km) heat production map for East Antarctica. Utilizing a Markov Chain Monte Carlo (MCMC) algorithm, we further develop a geothermal heat flow map with greater spatial variability than previous studies, yielding an average of $55\,$mW/m$^2$ in East Antarctica and $46\,$mW/m$^2$ in southwestern Australia. Our results provide a crucial high-resolution boundary condition for ice sheet simulations, enabling more realistic estimates of basal meltwater production and ice temperatures.