Why thermal stability of the carbonates of alkali metals increases down the group?

yes, the stability of carbonates increases down the group even though you would expect the lattice energy to decrease down the group. dont forget that the lattice energy of the products of decomposition of carbonates are metal oxides and CO2. and the stability(lattice energy) of oxides down the group decreases more than that for the corresponding carbonates. also note that the metal ions of higher atomic number are similar in size to the carbonate ion and fit better in the crystal structure. the metal ions with smaller atomic mass are more polarizing than the metal ions with large atomic mass (fajan`s rule) which means that they can attract the O- of carbonate ion better than the larger ions and hence are less stable as the stability mainly depends on the metal oxygen bond and not on the metal ion- carbonate ion attraction.across a period the stability decreases, again for the same reason.