Your motor only turns on because the furnace board feeds the fan board which then feeds the fan.. It is probably not temp controled but time controlled. You may have a dip switch on the fan board for adjusting the length of time that the fan runs. If you do see a dip switch and you adjust it and the fan runs on too long then it may feel drafty in your place. If you adjust the fan time too short then it will cost you in lost fuel efficiency. I mention this to see if a different dip switch setting makes the fan behave. Remember how it was initially set up so you can return it to it's original setting if the fan behavour doesn't improve.
The fan can also be triggered by a tripping limit through your furnace board but that is an unlikely cause at the end of the heating cycle..
The most common culprit is the fan relay on the board which can be sometimes jarred loose when stuck in one position or the other but not when it is fluttering like yours.