With the advancement of next-generation fighter aircraft, the escalating cooling demands of thermal management in aircraft and their engines are approaching the thresholds of conventional heat sinks, including ram air and fuel. A variable cycle engine (VCE), characterized by its third-stream design, facilitates potential multi-heat sink coordination within the fuel thermal management system (FTMS). Despite the use of decoupled VCE and FTMS modeling in previous research, the heat sink potential of internal secondary bypass air remains largely unexplored and unquantified, with its feedback effects on VCE energy efficiency also lacking rigorous investigation. Driven by the background, this study proposes a novel coupling of VCE and FTMS design. By leveraging multidisciplinary simulations, we provide the first quantitative analysis of the heat sink efficacy of secondary bypass air across representative flight missions and elucidate its synergistic mechanism with fuel. Investigations reveal that compared with ram air, secondary bypass air markedly reduces the thermal accumulation by 36.57%-74.06%. This improved thermal performance is accompanied by a 2.17%-4.10% decrease in the hot-return fuel flow. Intriguingly, the induced specific fuel consumption penalty throughout various typical flight missions consistently remains below 0.8%, thereby demonstrating the economic efficiency and sustainable benefits of employing secondary bypass air for thermal management. Furthermore, this study presents the first optimization strategy for allocating heat transfer area. Specifically, an area ratio of 0.6 between the ram air and secondary bypass air significantly lowers the system hot-return fuel temperature by 2.68%. This work validates quantitative evidence for secondary bypass air-FTMS coupling and establishes a foundation for system-level thermal management schemes in advanced fighter aircraft and engine designs.