Lennox G14 turning on for only 30 seconds issue

Hi Folks:
I have a Lennox G14 furnace that was manufactured in late 1991. The furnace works great, but I've noticed something that seems odd.
Everytime the furnace stops running once it's reached the desired room temperature, it stays off for about 5 minutes or so (which is normal)....then it turns back on again for 30 seconds...then back off again immediately. After another long pause for about another 5 - 10 minutes (which is normal), it kicks back on again like normal and stays on until the desired room temp is reached.
Why would this furnance turn on for only 30 seconds ? Is this normal, or is there something that is not right?
Thanks
Clark
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My American Standard in heating mode/gas, starts the blower, shuts it off then the burner lights then the blower comes back on. Sounds like a heat switch getting the last little bit out of the heat exchanger. Of course I could be wrong
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Fan limit switch needs to be addressed...and at that age, its normal.
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Thanks for the reply. How would I address this switch? Is there an adjustment that needs to be made? Where exactly is this 'fan limit switch'?
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