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Mössbauer absorption line tracking methodology, under a constant velocity strategy, is used for a quasi-continuous observation of the a-transition on slightly non stoichiometric Fe1+xS alloy. To this end, two strategies were applied: an intelligent absorption line tracking with a control algorithm that uses the data measured in the previous region to establish the position of the next partial spectral range; and a predetermined line tracking in which temperatureevolution of a partial spectral region of interest (ROI) is programmed. The latter uses results from the former, in order to achieve a quasi-continuous partial spectral observation. These experiments clearly demonstrate that line tracking allows a more efficient use of the radioactive source, as the effort is concentrated in a partial region of the spectra from which the desired information can be obtained.