That fan has only 2 cables, a black and red, for positive and negative, which means there it is either on or off depending on if it's plugged in or not. There is no thermometer inside measuring how hot the processor is.
Normal computers usually have a fan with 3-4 cables. Two for power, one for controlling the speed, and the last one tells the computer what speed the fan is currently spinning at.
To turn on the fan when the processor gets hot you'd need to write a script that turns on or off a gpio pin depending on the temperature, connect that to the control input of a relay, and connect the fan's negative to the pi's negative, the pi's positive to the input of the relay, and the relay's output to the fan's positive. DO NOT connect the fan directly into the controllable GPIO pins.
Also, it cannot get hot enough to cause damage to itself unless it's somewhere very hot, a lot hotter then room temperature.