The semiconductor disk laser (SDL) is a versatile laser source offering multiwatt-level output powers and diffraction limited beams. While an approach to thermal management based on substrate removal has led to tens of watts of output power in the $1\mu \text{m}$ region, the use of intracavity diamond heatspreaders for thermal management has enabled multiwatt performance levels to be achieved at wavelengths from the red to the mid-infrared. The modeling presented indicates that this dichotomy in approach arises from the ability of the heatspreader approach to bypass the thermal resistance of the mirror structure built into the SDL. The power scaling limitations of SDLs with heatspreaders are explored: nonaxial heat flow in the heatspreader is shown to limit the power scaling with pump spot radius. The critical roles of the pump spot size and output coupling on efficiency are experimentally investigated. An output power of 7 W in a 1060 nm SDL is achieved with the maximum output power achieved at a pump spot radius of $85\mu \text{m}$ .