The coolant temperature sensor in an Elise S2 Rover engine has changed over time. When Lotus started delivering the S2, the long style sensor was installed. This was replaced with the short style sensor.

You will have to check in your engine bay which sensor is installed in your engine. If you can see the brass bush protruding from the engine, you will know it's the long style sensor. Otherwise, it'll be the short one you'll need.

This sensor feeds the ECU with information, if you see an erratic display on the temperature gauge, you will have to keep in mind that the ECU is also getting erratic information, which can lead to erratic idling or other problems. Best is to swap the sensor as soon as you think the temperarure shown isn't right.