The analysis of exoplanetary atmospheres often relies upon the observation of transit or eclipse events. While very powerful, these snapshots provide mainly one-dimensional information on the planet structure and do not easily allow precise latitude-longitude characterizations. The phase curve technique, which consists of measuring the planet emission throughout its entire orbit, can break this limitation and provide useful two-dimensional thermal and chemical constraints on the atmosphere. As of today, however, computing performances have limited our ability to perform unified retrieval studies on the full set of observed spectra from phase curve observations at the same time. Here, we present a new phase curve model that enables fast, unified retrieval capabilities. We apply our technique to the combined phase curve data from the Hubble and Spitzer space telescopes of the hot Jupiter WASP-43 b. We tested different scenarios and discussed the dependence of our solution on different assumptions in the model. Our more comprehensive approach suggests that multiple interpretations of this data set are possible, but our more complex model is consistent with the presence of thermal inversions and a metal-rich atmosphere, contrasting with previous data analyses, although this likely depends on the Spitzer data reduction. The detailed constraints extracted here demonstrate the importance of developing and understanding advanced phase curve techniques, which we believe will unlock access to a richer picture of exoplanet atmospheres.