After the furance heats the house and everything shuts off, 2 sec. later the fan kicks on for about 2sec, then shuts off for 2sec. then kicks on again for 2sec. Then off. It does this every time the furnace has kicked on to heat the house. I replaced the thermostat and the problem still exists. Could the thermocouple be bad?

It is a defective or out of range fan or fan and limit control. They can be adjusted if you know what you are doing.