The order of thermal stability of carbonates of $\text{ IIA }$group is:

The carbonates become more resistant to decomposition as we move down the group and must be heated to higher temperatures. This indicates that ${\mathrm{MgCO}}_3$ enhances stability.
Therefore, the Group IIA carbonates' accurate stability ranking is ${\mathrm{BaCO}}_3>{\mathrm{SrCO}}_3>{\mathrm{CaCO}}_3>{\mathrm{MgCO}}_3$