The Second Cold War is a term generally used to refer to the period from 1979 to 1985. During this time, relations between the US and the Soviet Union deteriorated after having been relatively amicable during the period of detente. While the Soviet Union does bear a great deal of responsibility for this turn in the relationship, the problems were not only their fault.
The Soviet Union did do things that helped make the relationship much more delicate. The first of these was their invasion of Afghanistan in 1979. They also shot down a civilian Korean Air jetliner in 1983. These incidents (and particularly the invasion) helped to make relations with the West worse.
However, the West definitely played a role in the worsening relations. Prime Minister Margaret Thatcher of Britain (elected 1979) and President Ronald Reagan (elected 1980) both took hard lines against the Soviets. Reagan, for instance, pushed for a renewed arms race in hopes of harming the Soviet economy.
In these ways, both the Soviets and the West were responsible in roughly equal parts for the deterioration of the relationship.