Tafamidis, chemical formula C14H7Cl2NO3, is a drug used to delay disease progression in adults suffering from transthyretin amyloidosis, and is marketed worldwide under different tradenames as a free acid or in the form of its meglumine salt. The free acid (CAS no. 594839-88-0) is reported to crystallize as distinct (polymorphic) crystal forms, the thermal stability and structural features of which remained thus far undisclosed. In this paper, we present—by selectively isolating highly pure batches of Tafamidis Form 1 and Tafamidis Form 4—the full characterization of these solids, in terms of crystal structures (determined using state-of-the-art structural powder diffraction methods) and spectroscopic and thermal properties. Beyond conventional thermogravimetric and calorimetric analyses, variable-temperature X-ray diffraction was employed to measure the highly anisotropic response of these (poly)crystalline materials to thermal stimuli and enabled the determination of the linear and volumetric thermal expansion coefficients and of the related indicatrix. Both crystal phases are monoclinic and contain substantially flat and π-π stacked Tafamidis molecules, arranged as centrosymmetric dimers by strong O-H···O bonds; weaker C-H···N contacts give rise, in both polymorphs, to infinite ribbons, which guarantee the substantial stiffness of the crystals in the direction of their elongation. Complete knowledge of the structural models will foster the usage of full-pattern quantitative phase analyses of Tafamidis in drug and polymorphic mixtures, an important aspect in both the forensic and the industrial sectors.