Step 1: Thermal stability of hydroxides generally increases as we go up the group in the periodic table.
Step 2: In alkaline earth metal hydroxides, the thermal stability increases as the metal cation becomes smaller and more highly charged. This is because the lattice energy increases with smaller cations, making the hydroxide more stable.
Step 3: Therefore, the correct order of thermal stability is: \[ {Ba(OH)}_2 < {Sr(OH)}_2 < {Ca(OH)}_2 < {Mg(OH)}_2. \]