Cubic-phase CsPbI3 quantum dots (QDs) have been recently synthesized with merits of excellent optoelectronic performance. However, vital properties of cubic CsPbI3 including lattice dynamics and stability at high temperature remain poorly explored. We fabricate cubic CsPbI3 QDs and study their lattice dynamic and thermal stability to 700 K. We obtain Raman modes of cubic CsPbI3 QDs from 300 to 500 K at ultra-low-frequency range down to 15 cm-1, consistent with first-principles calculations. Above 550 K, the modification of Raman features suggests sample degradation. Consistently, temperature-dependent photoluminescence measurements indicate the absence of other luminescence phases up to 700 K. With increasing temperature, the CsPbI3 QD photoluminescence peak has a blue shift with exponentially decreasing intensity, showing faster electronic degradation than structural degradation. Our work provides detailed investigation of CsPbI3 QD lattice dynamics, band gap, and their high-temperature behavior, potentially useful for their emerging optoelectronic applications.