The common wisdom in the literature about clinker aggregate (CA) is that it improves the performance properties of mortar or concrete to some extent. The current study, in this context, investigated the physical characteristics and mechanical performances of alkali-activated composites (AACs) made entirely with CA. The CA was used in three particle sizes of 0–2 mm (named No.10), 2–4 mm (named No.5), and 4–8 mm (named medium). To examine the impact of the fine CA-size fraction on the characteristics of AAC, No.10 CA was partially replaced by No.5 CA up to 50%, while the content of the medium CA was kept constant in all AAC mixtures. Moreover, to evaluate the influence of the 8-h curing temperature on the performance of the AACs, different temperature-based curing strategies (ambient, 45, and 75 °C) were applied to the AACs. In the production of AACs, granulated blast furnace slag was employed as an aluminosilicate-rich raw material, and a sodium silicate and sodium hydroxide combination was used as an alkaline activator. Physical properties (flowability, water absorption, capillary water absorption, and dry unit weight), and 8-h strength performances (flexural and compressive) were determined. Furthermore, to monitor the influence of high temperatures on the characteristics of the AAC, the mixtures were exposed to elevated temperatures (200, 500, and 800 °C). In SEM image analysis, it was determined that spherical CSH gels were formed in the heat-cured AACs. It has been observed that the geopolymerization products decompose in AACs exposed to 800 °C. To evaluate statistically the experimental results, a multi-factor analysis of variance (ANOVA) was also applied. The results revealed that increasing the coarser fine aggregate fraction led to higher water absorption and apparent porosity capacities and lower unit weight. Besides, strength performance was improved by applying a heat-curing strategy to the AAC, whereas a decrease was observed by increasing the No.5 CA fraction. There was a remarkable reduction in compressive strength and considerable loss of mass when the AAC mixes were exposed to high temperatures.