Single-component azobenzene-based phototropic liquid crystals (PtLC) are promising materials that have started to be explored for photonic applications. One of the essential factors determining the applicability of these materials is the rate of the thermally driven cis-trans isomerization. In this paper, the kinetics of the thermal back cis-to-trans reaction in a pure 4-hexyl-4'-methoxyazobenzene (6-AB-O1) compound in its isotropic liquid and nematic phases is studied (the undoped LC). The reaction rate constants, activation energies and thermal activation parameters were determined based on spectroscopic studies. The reaction kinetics is compared to that measured for the compound dissolved in chloroform. The results demonstrate that the thermal back reaction depends on the phase and molecular environment of the cis-isomer. Moreover, the effect of temperature on the absorption spectra of 6-AB-O1 in its isotropic, nematic and crystalline phases is examined. The changes in the compound's absorption spectra in the respective phases have been correlated to the positional order parameter S.