When the furnace cools down after a heating cycle, a relay senses when the air going through drops below 90 degrees. Below 90, the relay should releace and shut the motor down.
Either the relay could be sticking, or it could be getting current through your new motor circuit. Hard to say without seeing.
If your thermostat has a fan switch, you could do some troubleshooting of the relay with and without the motor in the circuit. Or simply call in a repairman & blow $60
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