Different arenas of cold war did not convert into a hot war between the two alliances because of the concept of logic of deterrence and logic of restraint exercised by the two Superpowers. It implies that
1. Even if one of the Super power tries to attack and disable the nuclear weapons of its rivals the other would still be left with enough nuclear weapons to inflict unacceptable destruction.
2. Both sides have capacity to retaliate against an attack and to cause so much destruction that neither can afford to initiate war.
3. Both superpowers were expected to behave more rationally and in a responsible manner in the sense that they understood the risks in fighting wars which may create a massive destruction. So both the Superpowers exhibited restraint on their actions to prevent the cold war from escalating into a full fledged war.