Okay someone that knows about these things will be along after work and should be able to help. My guess is bad limit switch but I don't know what I'm talking about. Maybe that isn't what it is called.
Until someone else does dive in - how long has it been doing this?
First thing I would check is to see if you have 24vac to the g terminal of the furnace board when the heat is off the and blower is still running. If there is voltage there then you probably have a bad t-stat or a short in the stat wiring.
Otherwise it could be the furnace circuit board. Generally the blower should run for a minute or 2 after the heat call is satisifed and the burner goes out to extract the heat and cool the heat exchanger. I believe that this can determined by temp or more likely just a fixed time. It would depend on the model of your furnace and how it controls this to figure out if it is the main circuit board or something else.
A forum community dedicated to Do it yourself-ers and home improvement enthusiasts. Come join the discussion about tools, projects, builds, styles, scales, reviews, accessories, classifieds, and more! Helping You to Do It Yourself!