Which of the property increases towards bottom in a group?

Thermal stability and ionic character of alkali metal carbonates increases towards bottom in a group.

A tiny, strongly charged cation can quickly polarized the carbonate ion due to its large ionic radius. Down the group, the ionic radius of group I cations grows.

The cation is more densely charged the smaller its ionic radius. Consequently, the more effective it is at polarizing carbonate ions the group I cations polarized the carbonate ion to varying degrees in the following order:

$L{i}^{+}>{\mathrm{Na}}^{+}>K^{+}>R{b}^{+}$

The easier it is to weaken a carbon-oxygen bond in the carbonate and create carbon dioxide and oxide during heating, the more polarized the carbonate ion is.

Hence, option C is correct.