The NAO does not change the temperature of the Earth nor is caused by any change of temperature of the Earth.
This 'cycle' is nothing more than trade currents pinching off the flow of the equatorial counter current (or not). It's purely random. Since it takes a while for current positions to wander, it tends to last several months and generally occurs during the winter of the northern hemisphere (or the summer of the southern hemisphere), usually shifting as the Sun passes overhead on the way south.
The NAO is due to uneven heating of the Earth and naturally variable weather during equinox. Nothing more.
This equatorial current shift warmer water to either the eastern Pacific, or the western Pacific, leaving the other side exposed to colder water welling up from below.
El Nino is called the 'Christ Child', because warmer water is on the west Pacific, leaving colder (and nutrient) rich water welling up from below, improving fishing. Fish go where there is food. This effect is felt in winter in the northern hemisphere, which is typically around Christmas.
BTW, the Atlantic ocean has one too. It can easily affect weather in Europe.
Indeed, the Titanic sinking, although it was due to several factors including egregious errors by the captain and crew and the lack of standard procedures, was also due to the factor of icebergs moving further south than usual that year. This was probably due to a stronger than usual equatorial counter current at the time.
