Analysis of the trends and variability of climate variables and extreme climate events is important for climate change detection in space and time. In this study, the trends and variabilities of minimum, maximum, and mean temperatures, as well as five extreme temperature indices, are analyzed over Rwanda for the period of 1983 to 2022. The Modified Mann–Kendall test and the Theil–Sen estimator are used for the analysis of, respectively, the trend and the slope. The standard deviation is used for the analysis of the temporal variability. It is found, on average, over the country, a statistically significant (α = 0.05) positive trend of 0.17 °C/decade and 0.20 °C/decade in minimum temperature, respectively, for the long dry season and short rain season. Statistically significant (α = 0.05) positive trends are observed for spatially averaged cold days (0.84 days/decade), warm nights (0.62 days/decade), and warm days (1.28 days/decade). In general, maximum temperature represents higher variability compared to the minimum temperature. In all seasons except the long dry season, statistically significant (α = 0.05) high standard deviations (1.4–1.6 °C) are observed over the eastern and north-western highlands for the maximum temperature. Cold nights show more variability, with a standard deviation ranging between 5 and 7 days, than the cold days, warm nights, and warm days, having, respectively, standard deviations ranging between 2 and 3, 4 and 5 days, and 3 and 4, and, especially in the area covering the central, south-western, south-central, and northwestern parts of Rwanda. Temperature increase and its variability have an impact on agriculture, health, water resources, infrastructure, and energy. The results obtained from this study are important since they can serve as the baseline for future projections. These can help policy decision making take objective measures for mitigation and adaptation to climate change impacts.