It is simple to control a small fan with the Pi GPIO.
I use a simple transistor circuit (with only 3 inexpensive components).
I use the Pi 5V pin to power my fan, but this could be used with an external 12V supply for 12V fans.
This is suitable for fans which draw up to 500mA. Substitution of a power transistor could be used to power larger fans.
simulate this circuit – Schematic created using CircuitLab
The software is even simpler - only a single line needs to be added to
to switch the fan on at 60℃ - 60000 millicelcius (the default is 55℃ but you can select any temperature). The fan turns off when the temperature falls by 10℃.
This uses the
gpio-fan overlay (which has been available in the kernel since late 2018) and should be included in recent versions of Raspbian. (Read
/boot/overlays/README for description of this and other Device Tree overlays.)