Aims. The rotational spectral modulation (spectro-photometric variability) of brown dwarfs is usually interpreted as a sign indicating the presence of inhomogeneous cloud covers in the atmosphere. This paper is aimed at exploring the role of temperature fluctuations in these spectral modulations. These fluctuations could naturally arise in a convective atmosphere impacted by such diabatic processes as complex chemistry, namely, a mechanism recently proposed to explain the L/T transition: CO/CH4 radiative convection.Methods. After exploring the observed spectral-flux ratios between different objects along the cooling sequence, we used 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. We also explored the impact of CH4 abundance fluctuations on the spectral modulation of 2MASS 0136.Results. The spectral-flux ratio of different objects along the cooling sequence and the rotational spectral modulation within individual objects at the L/T transition have similar characteristics. This strongly suggests that the main parameter varying along the cooling sequence, namely, temperature, might play a key role in the rotational spectral modulations at the L/T transition. 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 a consequence we expect from CO/CH4 radiative convection as an explanation of 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 at different bandpasses in the atmospheres of hot Jupiters.Conclusions. Our results suggest that the rotational spectral modulation from cloud opacity and temperature variations are degenerate. If the nearly anti-correlated signal between different wavelengths is, indeed, a strong sign of a change in the temperature gradient, the detection of direct cloud spectral signatures, for instance, the silicate absorption feature at 10 μm, would help to confirm the presence of clouds and their contribution to spectral modulations (which does not exclude temperature variations or other mechanisms that may also be at play). Future studies considering the differences in the spectral modulation of objects with and without the silicate absorption feature may give us some insight into how to distinguish cloud-opacity fluctuations from temperature fluctuations.