Furnace comes on and heats properly. After it turns off the blower kicks on and off several times more times.

What is the type and age of your furnace

It's a carrier 58GP, over 20 years old.
I'd love to be able to fix this myself if its possible. Thanks

Okay first you say it heats properly correct the fan comes on intermittingly after that gas heat?
Well in that unit there is a fan limit switch that brings the fan on at a set temp (ie after the burners light and the heat exchanger warms up) then after the thermostat is satisfied the burners shutoff and the fan will run for a period until the fan limit reachs it's shutoff temperature I can describe the fan limit to you you can check it's settings and adjust accordingly however if it needs to be replaced getting a part and replacing it will take some work if your up to it I'm here...

I don't have a manual, so if you could tell me where to look for the fan limit switch, I will check it.
Thanks