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

In some recent experiments (Bestwick et al 2015 Phys. Rev. Lett. 114 187201, Chang et al 2015 Nat. Mater. 14 473-7) 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 the presence or absence of inelastic scattering even at temperature T  =  0.