During the Cenozoic, land ice and climate interacted on many different timescales. On long timescales, the effect of land ice on global climate and sea level is mainly set by large ice sheets in North America, Eurasia, Greenland and Antarctica. The climatic forcing of these ice sheets is largely determined by the meridional temperature profile resulting from radiation and greenhouse gas (GHG) forcing. As a response, the ice sheets cause an increase in albedo and surface elevation, which operates as a feedback in the climate system. To quantify the importance of these climate-land ice processes, a zonally averaged energy balance climate model is coupled to five one-dimensional ice sheet models, representing the major ice sheets. In this study, we focus on the transient simulation of the past 800 000 years, where a high-confidence CO2 record from ice core samples is used as input in combination with Milankovitch radiation changes. We obtain simulations of atmospheric temperature, ice volume and sea level that are in good agreement with recent proxy-data reconstructions. We examine long-term climate-ice-sheet interactions by a comparison of simulations with uncoupled and coupled ice sheets. We show that these interactions amplify global temperature anomalies by up to a factor of 2.6, and that they increase polar amplification by 94 %. We demonstrate that, on these long timescales, the ice-albedo feedback has a larger and more global influence on the meridional atmospheric temperature profile than the surface-height-temperature feedback. Furthermore, we assess the influence of CO2 and insolation by performing runs with one or both of these variables held constant. We find that atmospheric temperature is controlled by a complex interaction of CO2 and insolation, and both variables serve as thresholds for northern hemispheric glaciation.