This study systematically investigates the effects of BF and NS on the mechanical performance of concrete at ambient temperature, as well as its impact resistance and microstructural evolution following exposure to elevated temperatures. Compressive, flexural, and splitting tensile strengths of NS–BF hybrid concrete were measured under ambient conditions. Specimens were then subjected to thermal exposure from 20 °C to 800 °C to evaluate residual mass, surface integrity, impact performance, and microstructural characteristics. A two-parameter Weibull distribution model was applied to statistically analyze the number of impact blows under both ambient and elevated temperature conditions. The results show that NS–BF synergy markedly enhanced the mechanical and impact properties of concrete. The mix with 0.15% BF and 1.0% NS exhibited optimal static mechanical properties, while BF0.15NS1.5 achieved significant gains in initial cracking energy (W1) and final cracking energy (W2), increasing by 29.06% and 33.19% at 20 °C, and by 30.08% and 35.65% at 200 °C, respectively, compared to normal concrete. Impact resistance, however, deteriorated significantly above 400 °C due to severe thermal damage. The impact energy degradation index displayed a U-shaped trend with temperature, indicating a critical damage threshold around 400 °C. Additionally, this study develops an impact energy prediction model for different failure probabilities and elevated temperature conditions (20–400 °C), providing a robust theoretical foundation and practical guidance for the engineering design and application of NS–BF composite concrete under combined elevated temperature and impact loading.