Okay, I just returned from taking another much closer look and have, what I think, is the cause of the problem. I want to start off by asking you to excuse the way I'm going to describe things. There is a Honeywell thermostatic control(?) for the blower. I popped the cover off and saw a wheel that has 3 movable set points. The low set point is at 90 and the middle one is set at 130. If I recall, the max is set at around 200. I watched the operation of this device when the furnace came on. As expected, the furnace heated up the air, the wheel moved and the blower came on when the wheel turned and tripped the peg at 130. After about 45 seconds, the cold incoming air (the house was at 45 degrees) caused the wheel to turn and trip the lower peg (90 degrees) which, in turn, caused the blower to turn off again. This continued until I manually turned the heat off.
My question now is....am I going to cause any other problems if I adjust the low set point down to about 50 degrees? And, while I'm asking questions.....why is there a low set point to begin with?