  We investigate the finite-temperature phase diagram of the classical
Kitaev-Heisenberg model on the hexagonal lattice. Due to the anisotropy
introduced by the Kitaev interaction, the model is magnetically ordered at low
temperatures for all values of parameters at which the model has a discrete
symmetry. The ordered phase is stabilized entropically by an order by disorder
mechanism where thermal fluctuations of classical spins select collinear
magnetic orders in which magnetic moments point along one of the cubic
directions. We find that there is an intermediate phase between the
low-temperature ordered phase and the high-temperature disordered phase. We
show that the intermediate phase is a critical Kosterlitz-Thouless phase
exhibiting correlations of the order parameter that decay algebraically in
space. Using finite size scaling analysis, we determine the boundaries of the
critical phase with reasonable accuracy. We show that the Kitaev interaction
plays a crucial role in understanding the finite temperature properties of
A$_2$IrO$_3$ systems.
