Sounds like a bad gauge or sender.

Water Temperature Indicator Sender Unit
Removal and Installation

Drain engine cooling system.

Disconnect battery ground cable

On 2.5L engine equipped vehicles, remove air cleaner

Disconnect fuel charging wiring from water temperature indicator sender unit located on the water crossover (2.5L engine) or water thermostat housing (2.0L engine).

Remove water temperature indicator sender unit.

To install, reverse Removal procedure. Tighten water temperature indicator sender unit to 7-10 N-m (62-89 lb-in) on 2.0L engines. Tighten water temperature indicator sender unit to 18-24 N-m (13-18 lb-ft) on 2.5L engines.

1996 2.5LT V6 Contour ATX My Tour+help/info pics E0 rims, Gutted Pre-Cats,CTA Custom Exhaust & Intake, Diablo Chip.