Temperature Evolution of the Quantum Hall Effect in Quasi-One-Dimensional Organic Conductors

The Hall conductivity in the magnetic-field-induced spin-density-wave (FISDW) state of the quasi-one-dimensional organic conductors (TMTSF)$_2$X at a finite temperature is calculated. The temperature dependence of the Hall conductivity is found to be the same as the temperature dependence of the Fr\"ohlich current of a regular charge/spin-density wave. Predicted dependence $\sigma_{xy}(T)$ can be verified experimentally in the (TMTSF)$_2$X compounds if all components of the resistivity tensor are measured and the conductivity tensor is reconstructed.