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[en] Over the past few years, evidence has been accumulated in support of the existence of a thermal-like component during the prompt phase of gamma-ray bursts (GRBs). However, this component, which is often associated with the GRB jet's photosphere, is usually subdominant compared to a much stronger non-thermal one. The prompt emission of GRB 131014A—detected by the Fermi Gamma-ray Space Telescope (hereafter Fermi)—provides a unique opportunity to trace the history of this thermal-like component. Indeed, the thermal emission in GRB 131014A is much more intense than in other GRBs and a pure thermal episode is observed during the initial 0.16 s. The thermal-like component cools monotonically during the first second while the non-thermal emission kicks off. The intensity of the non-thermal component progressively increases until being energetically dominant at late time, similar to what is typically observed. This is a perfect scenario to disentangle the thermal component from the non-thermal component. The initial decaying and cooling phase of the thermal-like component is followed by a strong re-brightening and a re-heating episode; however, despite a much brighter second emission phase, the temperature of the thermal component does not reach its initial value. This re-brightening episode is followed by a global constant cooling until the end of the burst. We note that there is a shallower low-energy spectral slope than the typical index value +1, corresponding to a pure Planck function, which better matches with the thermal-like spectral shape; a spectral index around +0.6 seems to be in better agreement with the data. The non-thermal component is adequately fitted with a Band function whose low- and high-energy power-law indices are ∼−0.7 and <∼−3, respectively; this is also statistically globally equivalent to a cutoff power law with a ∼−0.7 index. This is in agreement with our previous results. Finally, a strong correlation is observed between the time-resolved energy flux, and the corresponding spectral peak energy, of the non-thermal component with a slope similar to the one reported in our previous articles. Assuming a universal relation between the time-resolved luminosity of the non-thermal component, and its rest frame which we derived from a limited sample of GRBs detected by Fermi, we estimate a redshift of ∼1.55 for GRB 131014A, which is a typical value for long GRBs. These observational results are consistent with the models in which the non-thermal emission is produced well above the GRB jet photosphere but they may also be compatible with other scenarios (e.g., dissipative photosphere) that are not discussed in this article.