Overheating?

Ive been having an on going problem with the temp guage on this car. Im just driving in the city and the problem has been getting worse the last few months. Today the guage was going up at a light then when I take off go down a little and when I parked the radiator fan wasnt even on. Today when I got home the guage was like around 3 quarters high and the radiator fan was on and stayed on and the guage stayed the same. Coolant is full and new radiator. No leaks, funny smells or smoke. My neibor said its a fan switch. What do you think