  We study critical properties of the Kitaev-Heisenberg model on the honeycomb
lattice at finite temperatures which might describe the physics of the quasi
two-dimensional compounds, Na$_2$IrO$_3$ and Li$_2$IrO$_3$. The model undergoes
two phase transitions as a function of temperature. At low temperature, thermal
fluctuations induce magnetic long-range order by order-by-disorder mechanism.
Magnetically ordered state with the spontaneously broken $Z_6$ symmetry
persists up to a certain critical temperature. We find that there is an
intermediate phase between the low-temperature ordered phase and the
high-temperature disordered phase. The finite-sized scaling analysis suggests
that the intermediate phase is a critical Kosterlitz-Thouless phase with
continuously variable exponents. We argue that the intermediate phase has been
actually observed above the low-temperature magnetically ordered phase in
Na$_2$IrO$_3$, and likely in Li$_2$IrO$_3$.
