High-temperature magnetic measurements have been carried out in hydrothermally synthesized greigite (Fe3S4). A high-vacuum environment for the magnetic measurement allows us to determine quite reliably the Curie temperature TC (about 677 K) of greigite. From the reported neutron and low-temperature magnetization data, we also determine the inter-sublattice exchange energy (3.05-3.51 meV) that can quantitatively explain the measured TC. Such quantitative agreement suggests that the two important fundamental parameters determined here are reliable and intrinsic. Furthermore, the half-metallic nature of this material and its possible spintronic applications are revealed by a comparison of the measured lattice constant and sublattice moments with calculations based on the ab initio density functional theory in the generalized gradient approximation.