Thermal stability of metal carbonates generally increases as we move up the group of alkali metals. This is because the lattice energy (or bond strength) of the carbonate increases as the size of the cation decreases.
Among the given options, \( \text{Li}_2\text{CO}_3 \) (Lithium carbonate) has the highest thermal stability due to the small size of the \( \text{Li}^+ \) ion, which results in a strong ionic bond and greater stability at higher temperatures.
Thus, the correct answer is Option (A): \( \text{Li}_2\text{CO}_3 \).