My furnace runs the correct amount of time, turns off. Then turns on & off 2 more times shortly afterward?

it could be a lose wire or a relay going bad if its not effecting the heat cycles or the blower,then let it run,i have seen units do that and its either the relay on the board or relay that calls the induction blower on the board is sort of expensive and its not hurting the operation of the furnace so they just left it alone and that was 2 years ago and its still running.

i'm assuming you mean just the blower turns on and off 2 more times after the regular heat cycle......if thats the case ,likely your fan control needs adjusted or replaced...the fan control is sometimes part of a dual control called a fan-limit control,,..in either case you are looking to adjust the "fan off" setting...its probably set for around 100deg,,meaning once the thermostat satisfies and turns off the flame,the fan control keeps the blower on until the temperature in the furnace cools down to 100deg......most likely the control is getting a little weak and turning the blower off too soon,when there is still too much heat left in the furnace....then the heat builds back up [ even with flame still off] ,,when it builds up to the "fan on" temp,the control turns the blower back on,but because there isnt really that much heat in the furnace overall [ flame still off] the furnace cools quickly and the blower cycles off,,evidently yours is doing this twice between heat cycles...with power turned off,locate the fan control [it might have a removable cover covering the adjustable settings ] and lower the "fan off" setting about 5 or 10 degrees...if you set it too low,it will run the blower too long at the end of the heat cycle,blowing "cool" air for a while..you have to find a setting that runs it long enough but not too long...usually a 2 or 3 minute run time after the flame turns off works well.....if you cant seem to get it right,then replace the control..if is a combination fan/limit control,i recommend having an hvac tech do it because sometimes the new control's connections are different,or there is a "jumper" that needs to be cut or removed for certain applications or equipment damage will result..........dan

It's probably Just the purge fan getting rid of non-combustibles in the chamber. This function is normal, however if you know for sure that it never did this before then read the manual and it will tell you the order of operation and what you listen for.

could be a sensor going bad. if its not affecting the heat cycle then its probably best left alone.

Is it gas or electric?