DC gearhead motor broken - too much heat on terminals while soldering?
Rather than actually melting something, if you softened the plastic you could have twisted one of the brushes away from the commutator. If you can figure that out (or inspect the brushes if there's a cooling hole) you may be able to apply more heat and twist it back.

Failing that, a small screwdriver can straighten the tabs holding the plastic cap in. Remove it carefully, realign the brushes and reassemble.  (On reassembly, look for a couple of holes in the plastic cap, for pins to hold the brushes clear of the commutator. Reassemble, then pull out the pins...) 

If the motor's dead anyway there's nothing to lose except the time spent taking it apart.