Sustainable construction promotes the use of recycled aggregates from the demolition of either old concrete structures or earthquake-damaged structures. This construction approach has a positive impact on concrete production by reducing the consumption of natural resources. In this context, the current paper focuses on the two aspects, both related to the concrete made with recycled aggregates processed from earthquake-waste and reinforced with short (chopped) basalt fibres, i.e. (1) the residual strength of such the material after a high-temperature cycle (up to 700 °C); and (2) the mechanical behaviour of the material as a part of a confined square specimen structure after a thermal cycle and then wrapped with a carbon fibre reinforced polymer (CFRP) sheet. The effects of basalt fibres on the mechanical behaviour are investigated by testing ordinary concrete (no recycled aggregates) and the concrete with 50% and 100% replacement ratios of recycled aggregates, in all cases before and after a thermal cycle. The results show that using basalt fibres significantly improves the concrete mechanical performance not only at room temperature but also after a thermal cycle, even for a small fibre content (less than 4 kg/m3). Also, the CFRP sheet significantly enhances the load-carrying capacity of the concrete specimen after subjected to a high temperature. In addition, a design-oriented model is formulated to evaluate the load-bearing capacity of CFRP-wrapped specimens with the temperature effect.