Enthalpy relaxation data obtained for amorphous selenium by means of fast scanning calorimetry were described in terms of Tool-Narayanaswamy-Moynihan model. The effect of thermal gradients formed within the measured sample was found to explain the marked difference between the FSC and conventional DSC data obtained for a-Se. If the influence of thermal gradients is accounted for, the similar set of TNM parameters as obtained for a-Se from conventional DSC can be used to describe the FSC data. Temperature profiles of the thermal gradients as well as sources of additional uncertainties occurring within the introduced conception are discussed in detail. In addition, a normalization procedure accounting for the difference between the slopes of heat capacity in the glass and undercooled liquid regions was introduced. Correct data preparation was found to have a critical influence on the applied enthalpy relaxation evaluation procedures. Due to the unresolved issue of the prediction of manifesting thermal gradients found in case of the recent study on amorphous selenium, the FSC technique appears, for the time being, to have limited usage for enthalpy relaxation studies.