Depending on the model, there may be subtle variations to the error code meaning for F13, but essentially it will mean "Dryer fan or dryer thermisotor faulty or open or short circuit."
There is a high probability it is a thermistor tripping out. It cuts power to the heater or fan, or both if the tumble dryer function overheats. If you take the top off the machine, somewhere in the area of the heating element, you will see the thermistor (There could be more than one). It's round, about the size of your thumbnail, set into an oval metal casing, usually with 2 holes in it to mount it and a couple of spade connectors coming off it..
(See a picture here: http://www.espares.co.uk/part/tumble-dryers/thermostats/indesit/isl70c/p/1587/805/0/552087/552036/tumble-dryer-thermostat-k.html
It may need replacement, or you may be able to reset it. If it is one that can be reset, the back will have a small hole in it that you can poke a paperclip end into.
Basically, the thermistor is a convex bi-metal disc that, when it gets too hot, pings and becomes concave, by pushing a paperclip into the hole, you push out the disc and make it concave again (You will hear it click as you push the pin in).
You can test to see if it is the thermistor that has tripped by bypassing it (Jump a wire from one spade to the other) and seeing if the machine then tumbles and heats as it should. DO NOT leave it like this! It is a fire risk as you will have bypassed the fail safe!.
Also ask yourself WHY it tripped in the first place. The primary cause is simply a blocked lint filter that is not allowing enough air passage and causing an overheat, but it could also be a faulty heater element that is burning out.
Hope this all helps