Si hyperdoped with chalcogens (S, Se, Te) is well known to possess unique properties such as an insulator-to-metal transition and a room-temperature sub-band-gap absorption. These properties are expected to be sensitive to a postsynthesis thermal annealing, since hyperdoped Si is a thermodynamically metastable material. Thermal stability of the as-fabricated hyperdoped Si is of great importance for the device fabrication process involving temperature-dependent steps such as Ohmic contact formation. Here, we report on the thermal stability of the as-fabricated Te-hyperdoped Si subjected to isochronal furnace anneals from 250 to 1200 degrees C. We demonstrate that Te-hyperdoped Si exhibits thermal stability up to 400 degrees C for 10 min, which even helps to further improve the crystalline quality, the electrical activation of Te dopants, and the room-temperature sub-band-gap absorption. At higher temperatures, however, Te atoms are found to move out from the substitutional sites with a maximum migration energy of E-M = 2.3 eV forming inactive clusters and precipitates that impair the structural, electrical, and optical properties. These results provide further insight into the underlying physical state transformation of Te dopants in a metastable compositional regime caused by postsynthesis thermal annealing. They also pave the way for the fabrication of advanced hyperdoped Si-based devices.