1998 Honda Accord Starter 'Sticks'

When I turn the ignition the vehicle starts but the starter stays engaged with the flywheel too long making the screetching noise you would expect. The point is that this especially true when it is cold outside. When its warm, the problem is hardly noticible. But the colder it gets, the longer the starter stays engaged prior to finally disengaging on its on. Sometimes for several seconds.
Sincere Thanks!