In thin-film light-emitting diodes (LEDs) absorption of the generated light in the substrate is avoided by the transfer of the epitaxial LED layers on a reflecting carrier. The extraction efficiency can be further enhanced by texturing the top surface. We developed a structure for high-efficiency surface-textured thin-film AlGaInP LEDs with improved heat dissipation by wafer-bonding onto a carrier substrate using conductive epoxy. The improved heat removal toward the substrate through the conductive epoxy increases the maximum allowable current density by more than a factor of two, compared to LEDs bonded on the carrier substrate with benzocyclobutene. As a result, an optical power of 65 mW is achieved for unencapsulated devices emitting at 650 nm. Using this technology, we also demonstrate an external quantum efficiency of 43\% for unencapsulated LEDs at a peak wavelength of 650 nm, which is the highest reported efficiency for AlGaInP thin-film LEDs. The external quantum efficiency increases to 52\% at 100 K