Why is my engine temperature gauge indicating my car is overheating as I drive?

What is your question?

My dad checked the anti-freeze and, while there is a small leak, there is still sufficient in the container. He thinks it may be the fan that is not working all the time. The indicator will rise to the overheating stage after I've been driving for about 5-15 minutes, but not every time I drive. I have noticed my fan sometimes does not work, but that too seems intermittent. What should I ask for or look for when I take it in to a service place? Could it be something my dad can do?