* Radioactivity: Astatine is a highly radioactive element. Its short half-life and intense radioactivity make it extremely difficult to study and handle. This limits our ability to accurately measure its thermal conductivity.

* Solid State: Astatine is a solid at room temperature, and its solid state is likely to be a poor conductor of heat due to its structure and the nature of its bonding.

* Halogen Group: Astatine belongs to the halogen group (Group 17) of the periodic table. Halogens are generally poor conductors of heat and electricity because their atoms are tightly bound together, making it difficult for heat or electricity to flow easily through them.

In summary, while we don't have definitive experimental data, based on its properties and position in the periodic table, it's safe to conclude that astatine is likely a very poor thermal conductor.