Actually all a fan will do is blow air not always the temperature desired. I am assuming you can see the runs.
Some Ideas... Try making a larger run or a second run to the room that is too cool.
Check very carefully that all in line dampers are all open first. Open all first. Then start closing the ones that appear too warm first. Leave the one in the cool room totally open. Check to see that the room is getting full air when the furnace is on. If the air seems less then other rooms there is a restriction in the run. 4" runs seem small to me (I live in northern Ohio). It could be a closed damper (and they can be very small to see from the outside of the run) or something lodged in the run. I have seen all kinds if things in ducts over the years (from toys to dead animals).
Check the cutoff timer on the furnace. Most newer furnaces have a set time the blower stays on after the burner shuts off. This can be adjusted and sometimes will prevent the blowing of cool air.
Insulate that run. Air will stay warmer (or cooler in summer)between cycles.
Hope this helps.