We analyze the energy balance climate model with CO2-dependent outgoing radiation, and obtain the steady-state solution for very wide range of the atmospheric CO2 partial pressure and the thermal diffusion coefficient. We propose a phase diagram of the climate on the parameter space of the atmospheric CO2 and the thermal diffusion coefficient for the latitudinal heat transport, which may be useful to understand the climate change through the history of the Earth. It is shown that the formation of polar ice caps can be caused by decrease in the atmospheric CO2 and the latitudinal heat transport. The different history of glaciation in each hemisphere through the Cenozoic might be the result of difference in the heat transport in each hemisphere. Understanding of the small ice cap instability might be important to interpret the oxygen isotope record at the Eocene-Oligocene boundary. ¿ 1999 American Geophysical Union