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Polar amplification of climate change is simulated across models with various representations of local feedbacks and poleward energy transports. Yet uncertainty in attribution remains due to the interactive nature of the physical drivers and the different perspectives afforded by different diagnostic methods. Here, the role of sea-ice processes, moist energy transport, and the seasonal cycle of insolation are systematically isolated in two models, an energy balance model and an idealized general circulation model. Filling this gap in the modeling hierarchy reveals that, compared to a simple ice-albedo feedback (temperature-dependent surface albedo), the addition of thermodynamic-ice processes and the seasonal cycle of insolation profoundly affects seasonal polar warming. Climatologically limited-extent ice in the warm season permits only small increases in absorbed solar radiation, producing weak warming, while thick, cold ice in the cold season enables a large radiatively forced response. Despite this enhanced winter warming, the annual-mean polar amplification is modestly reduced by thermodynamic-ice processes. When the effect of latent heat transport on the EBM’s diffusive representation of atmospheric energy transport is disabled, polar amplification is further reduced by a factor of 1.8 across the range of ice representations, suggestive of a nearly additive warming by ice and moist-transport processes. Together, the findings imply that sea-ice thinning leads to winter warming that would promote a positive lapse rate feedback and that the increase in moist energy transport would also lead, in more complex models, to additional warming via a water vapor feedback.