Despite the likely increasing co-occurrence of drought and heat stress, not least in equatorial regions, due to climate change, little is known about the combinational effect of these stresses on rice productivity and quality. This study evaluated the impact of simultaneous drought and temperature stress on growth, grain yield, and quality characteristics of seven rice cultivars from Rwanda, grown in climate chambers. Two temperature ranges—23/26◦ C night/day and 27/30◦ C night/day—together with single or repeated drought treatments, were applied during various plant developmental stages. Plant development and yield were highly influenced by drought, while genotype impacted the quality characteristics. The combination of a high temperature with drought at the seedling and tillering stages resulted in zero panicles for all evaluated cultivars. The cultivar ‘Intsindagirabigega’ was most tolerant to drought, while ‘Zong geng’ was the most sensitive. A “stress memory” was recorded for ‘Mpembuke’ and ‘Ndamirabahinzi’, and these cultivars also had a high content of bioactive compounds, while ’Jyambere’ showed a high total protein content. Thus, climate change may severely impact rice production. The exploitation of genetic diversity to breed novel rice cultivars that combine drought and heat stress tolerance with high nutritional values is a must to maintain food security.