This study aimed to investigate the strength and permeability properties of binary and ternary systems for producing concrete mixes with a cure time of 7, 28, 90, and 180 days under high ambient temperatures (about 35–45 °C). The key variables were silica fume (SF) and fly ash (FA) and the water-to-binder ratio (0.18 to 0.55) needed for cementitious systems of normal to ultra-high-performance concrete (UHPC). The tests were conducted under BS 1881 and ASTM C 1202. Further, a parametric study was conducted using isoresponse curves and predictive models developed in the study. After 28 days with 5% SF, the SF-binary concrete mixes showed significant gains in compressive strength, while 10% and 15% showed no significant gains. With a water–binder ratio of 0.55, concrete showed slightly higher strength gains than concrete with ratios of 0.16, 0.25, and 0.40. A 5% SF addition to 0.25-based concrete reduced permeability by 70%, which was marginal for 10% and 15%. However, higher SF content did not significantly affect concrete permeability with water–binder ratios of 0.55 and 0.40. The SF-FA ternary cementitious system of UHPC resulted in negligible permeability. With the developed model, the predicted–tested strength and permeability ratio was between 0.96 and 1.01. The isoresponse pattern of permeability changes at 6% SF content, while adding SF increases permeability significantly. The parametric analysis revealed that strength development deteriorates after 120 days regardless of whether SF is added at 10% or 15%.