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The objectives of this study were to: (1) evaluate possible deviations in annual and seasonal maximum (Tmx) and minimum (Tmn) temperatures, and, (2) determine the spatial pattern of these temperature changes. The study used statistical downscaling of the Coupled Model Intercomparison Project Phase 5 (CMIP5) global climate models (GCMs) under four representative concentration pathway (RCP) scenarios. Perfect prognosis statistical downscaling models, based on support vector machine (SVM), were developed for this purpose. Biases in the GCM simulations were corrected using quantile mapping (QM) and the data were then used to determine future temperature scenarios at different locations within Bangladesh. For most of the GCMs, the mean bias was close to zero and the Nash–Sutcliffe efficiency was above 0.58 for the downscaled temperature. Non-parametric hypothesis tests showed equality in median, distribution and variance values of the observed and downscaled temperature for all GCMs. Temperature projections from the models revealed an increase in Tmx by 1.3–2.3 °C, 1.3–2.9 °C, 1.5–3.1 °C, and 2.2–4.3 °C, and Tmn by 1.8–3.0 °C, 2.1–4.2 °C, 2.4–4.5 °C, and 3.2–5.1 °C under the four RCPs during the 2070–2099 period when compared with the 1971–2000 period. The greatest increase in Tmx and Tmn was found in the more northern regions and the lowest increase was found in the southeast coastal region. Tmn tended to increase in winter, while Tmx increased predominantly during summer. Uncertainty in the temperature projections was found to be greater during the latter part of the century. The rapid rise in temperature predicted for the northern part of Bangladesh (which is historically prone to temperature extremes) may cause an increase in the frequency of temperature-related extremes in this region.