12v PC fan and relay

Does anyone know is it possible to drive a fan directly from the Arduino through a relay? I am doing a temperature controller for college project. I have a 5V relay(G6K-2P) and an external 12V wall wart to power my fan. I connected the 2 coils of the relay to a digital pin and ground. Pin 6(common) is connected to the external 12V through breadboard and the output of my PC fan(12V 1.4W D-78106) is connected to the normally open(pin 5 i think). I see a lot of people use a diode and a NPN resistor but is this neccesary for simple on/off control???
Thanks for your help guys
Kevin
PS attached is very rough schematic

Hi, what is the current required to drive the coil of your relay, if its more than 20mA then you will need a transistor to do the switching. I personally would never drive a coil directly from an output. No matter what you have, if its a semiconductor activating an inductive like a coil, you will need a diode. Cathode to positive side of coil and Anode to negative side of coil, this will protect your arduino output from inductive spikes.

Tom..... :)

does it matter what the size of the diode is no??? yes checking it there the relay draws 21mA of current so maybe this is too high! and the transistor circuit do i need a resistor? thanks for your help!