Hydrophilic acrylamide-based hydrogels are emerging platforms for numerous applications, but our ability to fully exploit these materials is currently limited. A deepening of our understanding of molecular-level structure/property relationships in hydrogels is crucial to progressing these efforts. Such relationships can be challenging to elucidate on the basis of experimental data alone. Here, we use molecular simulations as a complementary strategy to reveal the molecular-level phenomena that govern the thermo-mechanical properties of hydrogels. We focus on acrylamide-based hydrogels cross-linked with N,N'methylenebisacrylamide, generated using our previously-established computational crosslinking procedure. We find the water content to be a key determinant in the elastic response of these hydrogels, with enhanced tensile and shear properties at low water content. However, we also find increasing water content enhances the hydrogel's thermal conductivity, with the dominant contribution arising from the non-bonded contributions to the heat flux. In addition, chemical cross-linking improved the heat transfer properties of the hydrogel, whereas a reduction in convective heat transfer was predicted with an increase in hydrogel crosslinking. Our simulations provide a rational basis for designing and testing customized hydrogel formulations for maximising both thermal conductivity and mechanical properties.