We investigate the coupling between the dynamics in the Gulf of Aqaba (Gulf of Eilat, northern Red Sea) and the exchange flow through the Straits of Tiran in response to seasonally varying surface fluxes and northern Red Sea hydrographic conditions. Because the gulf is a relatively small basin, winter mixing between the surface and intermediate layers occurs over most places in the gulf including in the vicinity of the straits, and leads to a maximal exchange flow in the strait. During the spring, warming in the Red Sea forces an influx of warm Red Sea water into the gulf, the surface layer is refilled, and consequently the exchange flow in the straits changes from a maximal to a submaximal flow regime. As a result, the dense wintertime water formation in the gulf and the exchange flow through the strait are strongly coupled on seasonal time scales. In addition, the hydrographic conditions in the northern Red Sea undergo strong seasonality. These characteristics prevent the direct application of current theories for strait-marginal sea systems, which commonly assume steady conditions in the "open ocean" side of the strait and/or an annual mean surface flux over the marginal sea. We explain why the exchange of volume and heat between the Gulf of Aqaba (Gulf of Eilat) and the northern Red Sea is larger during spring-summer despite the net surface buoyancy input into the gulf and why it diminishes during fall-winter despite the large buoyancy loss to the atmosphere. The applicability of the results to other systems is discussed.