Why would the temperature on a 1993 Plymouth Voyager 30 go up when parking and not when driving?

Because when your moving, air is moving at the radiator, cooling it down, thus cooling your coolant down, thus cooling your motor temperature down causing the coolant temperature sensor to pick up a lower reading and relaying it to the gauge. Depending on how high it is in "Park" you may have poor circulation, a broken or missing fan shroud, weak water pump impellers, low coolant, inactive coolant fans or a bad fan clutch.