Step 1: Use lattice energy reasoning:
The decomposition product is the oxide $\text{MO}$. The small $\text{Mg}^{2+}$ ion forms an oxide with a very high lattice energy, which pays for the breakdown of the carbonate.
Step 2: Compare the temperatures:
$\text{MgCO}_3$ decomposes at a fairly low temperature. The decomposition temperature rises down the group, and $\text{BaCO}_3$ needs over 1300 degrees C.
Step 3: Pick the answer:
The least stable carbonate is $\text{MgCO}_3$, option A.
Final Answer:
Carbonate stability rises down group 2, so MgCO3 is the least stable.
\[ \boxed{\text{(A) }\text{MgCO}_3} \]