I would say never, if possible.  If you spead the seed out well or use a seed tape then you shouldn’t have to thin.  Even if the carrots are a bit close together they will still grow.  Of course if you have a clump together you have to do something.  The problem is the dreaded carrot fly  once they get the smell of carrot from the thinnings (which they can detect from miles away!) they lash in, lay their eggs and that is the end of your carrots.  If you must thin then do it before the carrots are too big and remove the thinnings immediatly to the compost heap or the bin (far away from the carrot bed).  I would do this in the first 2 or 3 weeks to avoid disturbing the roots of the remaining carrots too much.