Solid electrolytes are crucial for next generation solid state batteries and Na<sub>3</sub>PS<sub>4</sub> is one of the most promising Na<sup>+</sup> conductors for such applications. In this contribution, we present a detailed investigation of the evolution in structure and dynamics of Na<sub>3</sub>PS<sub>4</sub> under the effect of temperature in the range 30 < T < 600 °C through combined experimental-computational analysis. Although x ray Bragg diffraction experiments indicate a second order phase transition from the tetragonal ground state (α, P-42<sub>1</sub>c) to the cubic polymorph (β, I-43m), pair distribution function analysis in real space and Raman spectroscopy indicate remnants of tetragonal character in the range 250 < T < 500 °C which we attribute to dynamic local tetragonal distortions. The first order phase transition to the mesophasic high temperature polymorph (γ, Fddd) is associated with a sharp volume increase and the onset of liquid like diffusive dynamics for sodium-cations (translative) and thiophosphate-polyanions (rotational) evident by inelastic neutron- and Raman- spectroscopies, as well as pair-distribution function and molecular dynamics. These results shed light on the rich polymorphism in Na<sub>3</sub>PS<sub>4</sub> and are relevant for a host of high performance materials deriving from the Na<sub>3</sub>PS<sub>4</sub> structural archetype.<br>