Since the inception of the Antarctic ice sheet at the Eocene-Oligocene Transition (~ 34 Myr ago), land ice has played a crucial role in Earth's climate. Through the ice-albedo and surface-height-temperature feedbacks, land ice variability strengthens atmospheric temperature changes induced by orbital and CO<sub>2</sub> variations. Quantification of these feedbacks on long time scales has hitherto scarcely been undertaken. In this study, we use a zonally averaged energy balance climate model bi-directionally coupled to a one-dimensional ice sheet model. The relative simplicity of these models allows us to perform integrations over the past 38 Myr in a fully transient fashion, using a benthic oxygen isotope record as forcing to inversely simulate CO<sub>2</sub>. Output of the model are mutually consistent records of CO<sub>2</sub>, temperature, ice volume-equivalent sea level and benthic δ<sup>18</sup>O. Firstly, we investigate the relation between global temperature and CO<sub>2</sub>, which changes once the model run has experienced high CO<sub>2</sub> concentrations. Secondly, we study the influence of ice sheets on the evolution of global temperature and polar amplification by comparing runs with ice sheet-climate interaction switched on and off. We find that ice volume variability has a strong enhancing effect on atmospheric temperature changes, particularly in the regions where the ice sheets are located. As a result, polar amplification in the Northern Hemisphere decreases towards warmer climates as there is little land ice left to melt. Conversely, decay of the Antarctic ice sheet increases polar amplification in the Southern Hemisphere in the high-CO<sub>2</sub> regime. Our results also show that in cooler climates than the pre-industrial, the ice-albedo feedback predominates the surface-height-temperature feedback, while in warmer climates they are more equal in strength.