A fan limits function is: to bring the fan on when the heat exchanger reaches a certain temperature to prevent cold air blowing at startup to shut the fan off after the burner is shut off to prevent cold air and to extract the maximun heat from the heat exchanger while cooling down the heat exchanger and to shut the burner off at a safe maximum if the blower does not come on.
You should not be play> Assuming that the dial on the fan/ limit switch is an accurate