It is a still open question how equilibrium warming in response to increasing radiative forcing (specific equilibrium climate sensitivity S) is depending on background climate. We here bring palaeodata-based evidence on the state dependency of S by using CO2 proxy data together with 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land-ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. In our setup, in which the radiative forcing of CO2 and of the land-ice albedo (LI) is combined (dR_[CO2,LI]), we find a state dependency in the calculated specific equilibrium climate sensitivity S_[CO2,LI] for most of the Pleistocene (last 2.1 Myr). In the Pliocene part (2.6–5 Myr BP) the CO2 data uncertainties prevents a well-supported calculation for S_[CO2,LI], but our analysis suggests that during times without large land-ice area in the northern hemisphere (before 2.82 Myr BP) the specific equilibrium climate sensitivity S_[CO2,LI] was smaller than during interglacials of the Pleistocene. If we develop for S an equation as a function of dR_[CO2,LI] we find S_[CO2,LI] in interglacials to be 2–2.7x larger than during glacial maxima, potentially indicating that equilibrium warming for CO2 doubling might be in the upper range of results compiled in the IPCC AR4.