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We use a large ensemble set of simulations and initialized model forecasts to assess changes in the initial-value seasonal predictability of summer Arctic sea ice area from the late-twentieth to the mid-twenty-first century. Ice thickness is an important seasonal predictor of September ice area because early summer thickness anomalies affect how much melt out occurs. We find that the role of this predictor changes in a warming climate, leading to decadal changes in September ice area predictability. In January-initialized prediction experiments, initialization errors grow over time leading to forecast errors in ice thickness at the beginning of the melt season. The magnitude of this ice thickness forecast error growth for regions important to summer melt out decreases in a warming climate, contributing to enhanced predictability. On the other hand, the influence of early summer thickness anomalies on summer melt out and resulting September ice area increases as the climate warms. Given this, for the same magnitude ice thickness forecast error in early summer, a larger September ice area anomaly results in the warming climate, contributing to reduced predictability. The net result of these competing factors is that a sweet spot for predictability exists when the ice thickness forecast error growth is modest and the influence of these errors on melt out is modest. This occurs at about 2010 in our simulations. The predictability of summer ice area is lower for earlier decades, because of higher ice thickness forecast error growth, and for later decades because of a stronger influence of ice thickness forecast errors on summer melt out.