A superconducting (SC) 1.5 GHz (3rd harmonic) cavity is being developed for lengthening bunch and improving beam lifetime in the Hefei Advanced Light Facility (HALF) storage ring. This SC cavity is excited by an electron beam with 350 mA current, 1 nC charge, and ~6.7 ps length. This contribution presents optimizations on such a SC harmonic cavity in detail. Through optimizations it has a low R/Q < 45 Ω, which has potential to achieve a good bunch lengthening. It utilizes a large-radius beam pipe which traps the fundamental (1.5 GHz, TM010) mode, but allows all other cavity monopole and dipole higher-order-modes (HOMs) to travel into a room-temperature RF absorber. All of harmful HOMs are strong-ly damped using a pair of silicon carbide (SiC) rings. In addition, preliminary thermal analysis on the SiC rings is also described in this contribution