Using a split-Hopkinson pressure bar test instrument with a temperature control device, in this work, silicone rubber was tested at different temperatures (−40 °C–200 °C) and different strain rates (1.2 × 10³ s⁻¹–7.2 × 10³ s⁻¹). The results showed that the dynamic mechanical properties of silicone rubber were strain-rate sensitive at different temperatures and the yield strength of the silicone rubber increased with an increase in the strain rate. At a higher strain rate, silicone rubber showed temperature sensitivity. With a decrease in the strain rate, the influence of temperature on silicone rubber gradually decreased. Differential scanning calorimetry analysis showed that silicone rubber had good thermal stability at high temperatures. When the temperature was as low as −40 °C, the silicone rubber underwent a glass transition, showing the characteristics of brittle materials.