| The blower is controlled by a relay and timers or limit switches. On a heat cycle, the gas comes on, and then blower after a time or a temperature is reached. After the gas goes off, again either time or temperature shuts the blower off later. The off delay could be bad, or there could be a problem on the board. Most blower problems are due to a relay problem, but usually it is a problem of the relay either staying open or closed, not opening and closing on its own.
One other possible problem is a short between the contacts on the back of the thermostat. It does have a back that stays on the wall when you pull it? Pull the back off and look for any possible way for power to get from the red wire to the green wire. Also check at the furnace when the blower is running. See it you have 24 volts between the green and blue contacts.
Usually there is a 24 volt AC transformer in the furnace with the secondary winding connected to a red wire running to the thermostat and a blue wire, common, to the gas valve, A/C relay, and fan relay. From the thermostat there will be white wire to the gas valve, yellow to the A/C, and green to the fan. The thermostat is wired to switch the power from the red to the white, yellow, and green as needed with the blue completing the circuit. Most thermostats and furnaces have the contacts labeled R, B or C, W, Y, and G for the corresponding wire colors. It may be wired to have the A/C control wires return to the furnace and its controls and then a second wire goes to the A/C unit. Internal wiring may replace the green wire if the thermostat does not give you the option of fan only or continuous fan. Digital or programmable thermostats may need | 
Linear Mode
