The early Eocene was characterised by much higher temperatures and a smaller equator-to-pole surface temperature gradient than today. Comprehensive climate models have been reasonably successful in simulating many features of that climate in the annual average. However, good simulations of the seasonal variations, and in particular the much reduced Arctic land temperature seasonality and associated much warmer winters, have proven more difficult. Further, aside from an increased level of greenhouse gases, it remains unclear what the key processes are that give rise to an Eocene climate, and whether there is a unique combination of factors that leads to agreement with available proxies. Here we use a very flexible General Circulation Model to examine the sensitivity of the modelled climate to differences in CO2 concentration, land surface properties, ocean heat transport, and cloud extent and thickness. Even in the absence of ice or changes in cloudiness, increasing the CO2 concentration leads to a polar-amplified surface temperature change because of increased water vapour and the lack of convection at high latitudes. Additional low clouds over Arctic land generally decreases summer temperatures and, except at very high CO2 levels, increases winter temperatures, thus helping achieve an Eocene climate. An increase in the land surface heat capacity, plausible given large changes in vegetation and landscape, also decreases the Arctic land seasonality. In general, various different combinations of factors -- high CO2 levels, changes in low-level clouds, and an increase in land surface heat capacity -- can lead to a simulation consistent with current proxy data.