Heat sinks have manifold applications, from micro-electronics to nuclear fusion reactors. Their performance expectations will continue to increase in line with the power consumption and miniaturisation of technology. Additive manufacturing enables the creation of novel, compact heat sinks with greater surface-to-volume ratios and geometrical complexities than standard pin/fin arrays and pipes. Despite this, there has been little research into the use of high surface area lattice structures as heat sinks. Here, the hydraulic and thermal performance of five surface-based lattice structures were examined numerically. Computational fluid dynamics was used to create useful predictive models for pressure drop and volumetric heat transfer coefficients over a range of flow rates and volume fractions, which can henceforth be used by heat transfer engineers. The thermal performance of surface-based lattices was found to be heavily dependent on internal geometry, with structures capable of distributing thermal energy across the entire fluid volume having greater volumetric heat transfer coefficients than those with only localised areas of high heat transfer and low levels of fluid mixing.