Abstract. Climate is usually considered to depend on a large number of parameters, this being essentially a functional in multi-dimensional parameter space. We propose a low-dimensional model of a climate where the temperature field on a thermally conducting planet depends on the external energy input and very limited number of internal parameters, like thermal conductivity and reflectivity. Equilibrium temperature and quasistatic variations of climate following slow variations of the energy input are studied. The single phase model exhibits adiabatic behavior and stability with respect to small axisymmetric perturbation. The two phase model shows a non-trivial response to the variations of the external parameter. History dependence, global instabilities and hysteresis behavior characterize the surface temperature evolution.