pls help: gas furnace short-cycling ...

This morning I noticed it again: Setting the thermostat to 68 with my house at 63 degrees, the 18-year old Day-and-Night fired up beautifully, ran about five minutes, and then turned off the flame and soon afterwards the blower. Before the blower stopped the gas pilot had already ignited to resume. Three or four such short cycles ensued. Then -- miraculously -- the furnace stayed on for a full 45 minutes (it's still running) without interruption.
I'm sure this is an easy diagnosis for any gas furnace guru. Please share your thoughts!
Many thanks, Herb
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I'm the tech. Thanks a bunch! I'll send your check immediately to AA. -Herb
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