We present improved thermal management of an optically-pumped vertical external cavity surface emitting laser (VECSEL) at a center wavelength of around 2 µm. This was achieved with a backside-cooled, InGaSb-based VECSEL using a hybrid metal-semiconductor Bragg reflector. We demonstrate the fabrication of such a hybrid metal-semiconductor mirror by combining a copper mirror with 10.5 AlAs_0.08Sb_0.92/GaSb distributed Bragg reflector (DBR) pairs. Together with a thin 20 nm SiO₂ diffusion barrier we reach >99.9 % reflectivity at 2 µm. This allows for a thinner gain chip design compared to the standard DBR requiring 19.5 layer pairs. The structure thickness was reduced from 7.5 µm to 4.7 µm lowering the thermal resistance of the device from (2.79±0.16) K W⁻¹ to (2.12±0.19) K W⁻¹. We demonstrate record high average continuous wave (cw) output powers of 3 W for backside-cooled InGaSb-based VECSELs.