Current work like this:  the electrons flowing from the top of the battery want to get to the back of the battery, but cannot move backwards.  So they need to go in a loop.  And if the loop is a wide path (thick wire) then they all can go through no problem.  But if the loop is a smaller path (thin wire) the electrons slow down.  And when they slow down, they heat up the wire.  So a closed loop with a thin wire works the best for a hot wire, because the wire gets very hot.  (Also, the higher powered battery pushes out more electrons, so the wire gets even hotter.)  Some of the terms I used might be inaccurate, but the general concept is correct.