Are thermal fluctuations the sole reason for finite longitudinal resistance in quantum anomalous Hall experiments?

In some recent experiments [A. J. Bestwick, et. al., Phys. Rev. Lett. 114, 187201 (2015), Cui-Zu Chang, et. al., Nat. Materials. 14, 473-477 (2015)] it has been shown that in observations of the quantum anomalous Hall (QAH) effect the longitudinal resistance $R_L$ increases as temperature $T$ increases, while Hall resistance $R_H$ loses its quantization with increase in $T$. This behavior was explained due to increased thermal fluctuations as $T$ increases. We show that similar effects arise in QAH samples with quasi-helical edge modes as disorder increases in presence of inelastic scattering or otherwise even at temperature $T=0$.