The fan for the heater comes on and off at random times. Most of the time it will not work, then all of a sudden it comes on. I have an 07 plate Fiat Grande Punto.

Most likely the blower motor has excessive wear and the brushes which contact the armature are contacting more than one pole at a time, hence the intermittent failure. Hit a bump, or hit the motor, and it'll suddenly come on... Pretty typical really.

I'd say under the hood, passenger side firewall near the heater blower. A plate with multiple wires attached mounted on the air plenum. It is usually mounted in the airstream of the heater fan to keep it cooled.

The heater/blower fans in cars made since at least 1982 are designed to run at all times, even if in so-called "off" position. This may be because this fan is also for general air circulation and for the A/C. Don't know why. In the summer I would actually unplug the fan wire at the firewall (this was on a 1982 Buick). This was the advice of my mechanic. He said wiring in a toggle was more trouble than just unplugging the wire.

Possibly a leaking vacuum hose or connection to your heater control. Depending on engine vacuum, heat may appear to be going on and off, but might actually be going back and forth from defrost to heat. I have an 07 F350 that does this sometimes. If the heater fan itself is actually starting and stopping, could be a loose connection or a fan that is on its last legs.

Try looking for a bad batt connection

What is a plate?

Due to the age of your vehicle, the brushes in the fan motor are worn out. you will have to replace the fan motor, it is not serviceable.

its the blower motor resistor that is faulty or the blower motor resistor wire connector that has a bad connection.Wiggle the wire connector going to the resistor with the ignition switch and the fan switch in the on position and if the fan comes on then the connection is bad but, if it does'nt come on then the resistor is faulty.

Check your fuses. That would definitely be my first guess. Take one out for the wipers or something time being and pop it in and see if your fan doesn't fire right up. 

heater fan speed switch located in heater box by passengers feet up in heater box one plug on it cant miss two screws hold it in!!!!