If your vehicle is showing temperature gauge stays cold after driving, here are the most likely causes and the parts you'll need to fix each one.
The thermostat regulates engine temperature by restricting coolant flow until the engine warms up. If it fails in the open position, coolant flows constantly to the radiator, overcooling the engine and preventing it from reaching normal operating temperature.
The sensor that measures the coolant temperature has failed or has a bad connection. The engine is actually warming up properly, but the sensor is sending a dead or incorrect signal to the dashboard gauge.
If the coolant level is low or the system wasn't properly bled after recent work, an air pocket can form around the temperature sensor. Because air doesn't transfer heat to the sensor like liquid coolant does, the gauge reads cold even if the engine is dangerously overheating.
Sometimes a previous owner or mechanic removes the thermostat entirely to mask an overheating issue, or installs it backwards. This allows unrestricted coolant flow and prevents the engine from ever warming up properly.
The physical gauge on your dashboard or the internal circuitry controlling it has failed. The engine is warm and the sensor is working, but the needle mechanism itself is broken.