In a gas furnace, the blower will continue to run if the fan switch on the thermostat is set to any setting other than auto. The blower on a furnace will also continue to run if its filter is extremely clogged.
When the furnace's thermostat is set to auto, the fan will only run until the space that is being heated or cooled reaches the preset temperature. Settings such as low, medium or high cause the fan to run continuously regardless of the temperature that is reached in the space.
A clogged filter may cause the furnace's blower to run continuously because it can damage the furnace's limit switch. The limit switch is designed to detect the temperature inside of the furnace. It automatically shuts off the fire in the furnace if the temperature becomes too high until the furnace has the chance to reach a safe temperature.
A clogged filter also restricts the air flow inside the furnace. This causes the safety switch to remain open, causing the fan to run continuously. The fan will not stop until the safety switch closes. In this case, a fan that continues to run is a sign that the furnace has overheated.