Recent ice loss on the western Antarctic Peninsula has been driven by warming ocean waters on the continental shelf. However, due to the short observational record, our understanding of the dynamics and variability in this region remains poor. High-resolution ocean model simulations show that the temperature variability along the western Antarctic Peninsula is controlled by the rate of dense water formation in the Weddell Sea. Passive tracer advection reveals connectivity between the Weddell Sea and the coastline of the western Antarctic Peninsula and Bellingshausen Sea. During multi-year periods of weak Weddell dense water formation, dense overflow transport in the Weddell Sea decreases, while the transport of cold water around the tip of the Antarctic Peninsula strengthens, driving a temperature decrease of 0.4^oC along the western Antarctic Peninsula. This mechanism implies that western Antarctic Peninsula coastal ocean temperature may cool in the future if Weddell Dense Shelf Water production slows down.