Does the blower on your furnace stay on constantly, i.e. never turning off?
Most theromostats have a setting on the fan for “fan continuous” which, if enabled, explains why the blower doesn’t turn off. Go ahead and change the setting off of fan continuous if this is the case.
If the setting is not the issue with the blower staying on, the problem is most likely a faulty fan limit control switch and this will need replacement. We strongly suggest you call your heating expert for repair.