Cubic boron arsenide (BAs) is attracting greater attention due to the recent experimental demonstration of ultrahigh thermal conductivity k{appa} above 1000 W/mK. However, its bandgap has not been settled and a simple yet effective method to probe its crystal quality is missing. Furthermore, traditional k{appa} measurement methods are destructive and time consuming, thus they cannot meet the urgent demand for fast screening of high k{appa} materials. After we experimentally established 1.82 eV as the indirect bandgap of BAs and observed room-temperature band-edge photoluminescence, we developed two new optical techniques that can provide rapid and non-destructive characterization of k{appa} with little sample preparation: photoluminescence mapping (PL-mapping) and time-domain thermo-photoluminescence (TDTP). PL-mapping provides nearly real-time image of crystal quality and k{appa} over mm-sized crystal surfaces; while TDTP allows us to pick up any spot on the sample surface and measure its k{appa} using nanosecond laser pulses. These new techniques reveal that the apparent single crystals are not only non-uniform in k{appa}, but also are made of domains of very distinct k{appa}. Because PL-mapping and TDTP are based on the band-edge PL and its dependence on temperature, they can be applied to other semiconductors, thus paving the way for rapid identification and development of high-k{appa} semiconducting materials.