that are a number of reasons to this problem
overheating, coolant leak fuel line problem exhaust problem and also you should be checking for vacuum leaks and make sure the IAC is working properly.
IAC is idle air control.which is a solenoid that is responsible for maintaining engine idle.
More than likely air speed control switch is gone bad. Before changing that have a look in engine bay fuse box relay for blower isnt blacked out. If it is then change that first and see if it helps.
Along with gti points, also check AC fan is working. As while idle car overheat due to AC load too and while running as gti explained car radiator get air cooled automatically.