  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.
