The correct order of increasing thermal stability of K2CO3,MgCO3,CaCO3 and BeCO3 is:
BeCO3<MgCO3<CaCO3<K2CO3
Between K2CO3 and CaCO3, the former is much more stable thermally. This is because the potassium cation is 'softer' owing to the larger size plus lower charge density. According to the Hard-Soft Acid-Base or HSAB theory, similar anions and cations - a soft cation paired with a soft anion OR a hard cation paired with a hard anion - come together to produce more stable chemical substances. Hence, the correct order is BeCO3<MgCO3<CaCO3<K2CO3
As we go down the group, the thermal stability of alkaline earth carbonates increases. This can also be explained using the HSAB theory.