The climate change will contribute drought and temperature extremes to rice growing systems, especially when cultivated in equatorial regions. To evaluate opportunities to cultivate and breed drought-tolerant rice, seven rice cultivars were evaluated in Rwanda for recurring morphological drought scores, grain yield and components, and quality characteristics. The cultivation conditions, that is site and drought treatment, impacted morphological drought scores, growth and yield attributes, while cultivar affected quality attributes. Thus, site showed a higher impact on grain yield and components than drought and cultivar, with generally a reduced grain yield at the low-temperature site, as a result of low spikelet fertility. Morphological drought scores were generally increased by drought, while drought at the reproductive stage at the high-temperature site was negative for yield and its components. The cultivars “Intsindagirabigega” and “Jyambere” were adapted to high-temperature site conditions. The cultivar “Intsindagirabigega” had the highest amylose content, and “Mpembuke,” the highest antioxidant capacity. Thus, climate change with increased temperature and drought extremes may increase rice productivity in cool areas, while especially drought at reproductive stage will be detrimental in low altitude areas with high temperature. Cultivar variation indicated opportunities for selection and breeding of climate change tolerant rice cultivars which should be of immediate priority.