After decades of research, recent laser-driven inertial fusion experiments have demonstrated rapid progress towards achieving thermonuclear ignition using capsule designs with cryogenic fuel layers. The ignition physics for these layered capsules involves a complex interplay between the dynamically forming hot spot and the dense surrounding fuel. Using analytic theory, we demonstrate that the mass ablation rate into the hot spot depends sensitively upon the temperature of the dense fuel, resulting in ablative inflows up to 4× faster than previous estimates. This produces an enthalpy flux into the hot spot which plays a critical role in controlling the hot spot temperature, the ignition threshold, and the subsequent burn propagation. The net influence of mass ablation on the ignition threshold is regulated by a dimensionless parameter which depends upon the temperature of the dense fuel. As a consequence, the ignition threshold is sensitive to any mechanism that heats the dense fuel, such as neutrons or radiation emitted from the hot spot. These predictions are confirmed using radiation hydrodynamic simulations for a series of capsules near ignition conditions. This analysis may have relevance for understanding the variable performance of recent experiments and for guiding new capsule designs toward higher fusion yields.