I have seen tutorials that show a fan plugged into the USB port to cool the Pi, would this overload the Pi? Is it necessary to use a fan at all?
Generally speaking a cooling fan is not required for the safe operation of a Raspberry Pi.
The cooling fan would probably plug into the GPIO or USB, I've used a fan that is rated at 5V and 0.2A with my Pi 2. It reduced the temperature slightly but not significantly. Certainly not significant enough to warrant the noise the fan produced.
The Pi has a thermal limit of 85°C, when it reaches this temperature it will limit the performance of the CPU to reduce the temperature.
I think it is unlikely that you will ever reach this temperature unless you are either doing some serious overclocking or running the CPU at 100% for sustained periods of time.
If you do want to use a cooling fan make sure the Pi is adequately powered. You need to use a power supply that can reliably deliver 5V at 2A. Also to improve the cooling performance you could add a heatsink to the SoC and the Ethernet controller. Since these are the two chips on the board that tend to get the hottest.