Polymorphism and temperature-induced phase transitions of Na2CoP2O7 were studied by in situ neutron powder diffraction and complemented by ab initio calculations to reconcile previous reports of its three polymorphs. We show that the "blue" form prepared at 873 K exists at room temperature in the orthorhombic Pna2(1) (= P2(1)cn) phase, which transforms via a first-order transition to the tetragonal form at the temperature close to room temperature (similar to 335 K). Just above the transition, the tetragonal form is likely incommensurately modulated with the modulation vanishing at similar to 423 K. Above that temperature the phase remains in the unmodulated tetragonal state (P4(2)/mnm) until melting at similar to 900 K. Upon cooling after melting, Na2CoP2O7 crystallizes into the "rose" triclinic P1 form which persists while it cools to room temperature, apparently stabilized by the barrier of the reconstructive "rose-blue" transition. We also discuss the relationship between the tetragonal and orthorhombic structures, the driving forces of the orthorhombic distortion, and similarity to Na2ZnP2O7 and the melilite-type structural family.