We report the preliminary demonstration of continuous wave (cw) GaSb-based interband cascade lasers (ICLs) with hybrid cladding layers at high temperatures up to 80 degrees C near a wavelength of 3.72 mu m. These ICLs have narrow-ridge widths of 7-11 mu m with improved thermal dissipation compared to broad-area devices. They delivered a cw output power of more than 30 mW/facet at 20 degrees C and had a cw threshold current density of 270 A/cm(2) with a voltage efficiency of 78% at 300 K. The obtained voltage efficiency of 78% is the highest ever reported among cw GaSb-based ICLs at room temperature, indicating an advantage of efficient carrier transport in the ICL with the hybrid cladding layers. The dependence of device performance on the narrow-ridge width and cavity length was investigated. The results suggested ways to further improve future devices.