group 1 and group2 metal

Do you mean the stability of the oxide/carbonate of the metal or the metal itself?

For metal itself, the group one and two metals should be quite stable towards heating as they are both coated with oxide layer. Yet their melting point is relatively low when comparing with other metals. The group one metal generally have lower melting point than the group two metal of the smae period due to its weaker metallic bond.

The oxide of both group are expected to be stable towards heat.

The carbonate of group two is expected to decompose at a lower temperature than that of group one metal of the same period due to the higher distortion power of the doubly charged group two ion.

Obviously the one of the reasons for putting potassium superoxide in manned space capsules aims at removing excessive carbon dioxide from the capsule while providing oxygen for the astronaut in the capsule.