How can we compare thermal stability in HClO,HClO2,HClO3,HClO4?

For thermal stability, there are two main reasons to understand the order that HClO<HClO2<HClO3<HClO4.

1)A higher oxidation number of the central chlorine atom means a more positive charge in the Cl atom, which will increase the bond strength between the Cl atom and the O (or OH) ligands.
Secondly, the stability of a substance is related to the structural symmetry. More the symmetry, more the stability.