The rotational spectral modulation (spectro-photometric variability) of brown dwarfs is usually interpreted as a sign of the presence of inhomogeneous cloud covers in the atmosphere. This paper aims at exploring the role of temperature fluctuations in these spectral modulations. These fluctuations could naturally arise in a convective atmosphere impacted by diabatic processes such as complex chemistry, i.e. the recently proposed mechanism to explain the L/T transition: CO/CH4 radiative convection. We use the 1D radiative/convective code ATMO with ad-hoc modifications of the temperature gradient to model the rotational spectral modulation of 2MASS 1821, 2MASS 0136, and PSO 318.5-22. Modeling the spectral bright-to-faint ratio of the modulation of 2MASS 1821, 2MASS 0136, and PSO 318.5-22 shows that most spectral characteristics can be reproduced by temperature variations alone. Furthermore, the approximately anti-correlated variability between different wavelengths can be easily interpreted as a change in the temperature gradient in the atmosphere which is the consequence we expect from CO/CH4 radiative convection to explain the L/T transition. The deviation from an exact anti-correlation could then be interpreted as a phase shift similar to the hot-spot shift a different bandpasses in the atmosphere of hot Jupiters. Our results suggest that the rotational spectral modulation from cloud-opacity and temperature variations are degenerate. The detection of direct cloud spectral signatures, e.g. the silicate absorption feature at 10 um, would help to confirm the presence of clouds and their contribution to spectral modulations. Future studies looking at the differences in the spectral modulation of objects with and without the silicate absorption feature may give us some insight on how to distinguish cloud-opacity fluctuations from temperature fluctuations.
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