Abstract. Analysis of the 3.6 Ma, 318 m long sediment core from Lake El'gygytgyn suggests that the lake was covered by ice for millennia at a time for much of its history and therefore this paper uses a suite of existing, simple, empirical degree-day models of lake-ice growth and decay to place quantitative constraints on air temperatures needed to maintain a permanent ice cover on the lake. We also provide an overview of the modern climatological and physical processes that relate to lake-ice growth and decay as a basis for evaluating past climate and environmental conditions. Our modeling results indicate that modern annual mean air temperature would only have to be reduced by 3.3 °C ± 0.9 °C to initiate a multiyear ice cover and a temperature reduction of at least 5.5 °C ± 1.0 °C is likely needed to completely eliminate direct air–water exchange of oxygen, conditions that have been inferred at Lake El'gygytgyn from the analysis of sediment cores. Once formed, a temperature reduction of only 1–3 °C relative to modern may be all that is required to maintain multiyear ice. We also found that formation of multiyear ice covers requires that positive degree days are reduced by about half the modern mean, from about +608 to +322. A multiyear ice cover can persist even with summer temperatures sufficient for a two-month long thawing period, including a month above +4 °C. Thus, it is likely that many summer biological processes and some lake-water warming and mixing may still occur beneath multiyear ice-covers even if air–water exchange of oxygen is severely restricted.