The design of an aircraft thermal management system (TMS) that is capable of rejecting heat loads into the bypass stream of a typical low-bypass ratio turbofan engine, or a ram-air stream, is investigated. The TMS consists of an air cycle system, similar to the typical air cycle machines used on current aircraft, both military and commercial. This system turbocharges compressor bleed air and uses heat exchangers in a ram air stream, or the engine bypass stream, to cool the engine bleed air prior to expanding it to low temperatures suitable for heat rejection. In this study, a simple low-bypass ratio afterburning turbofan engine was modeled in numerical propulsion system simulation to provide boundary conditions to the TMS system throughout the flight envelope of a typical military fighter aircraft. Two variations of the TMS system, a ram air cooled and a bypass air cooled, were sized to handle a given demanded aircraft heat load. The ability of the sized TMS to reject the demanded aircraft load throughout several key off-design points was analyzed. It was observed that the maximum load dissipation capability of the TMS is tied to the amount of engine bleed flow, while the level of bleed flow required is set by the temperature conditions imposed by the aircraft cooling system. Notably, engine bypass stream temperatures significantly limit the thermodynamic viability of a TMS designed with bypass air as the heat sink. The results demonstrate the advantage that variable cycle engines (VCEs) may have for future aircraft designs.