It would appear there is a problem with the sensor, the wiring or the gauge. I hope this helps. Here is my experience with the temperature gauge on my 5210. When I purchased the tractor the needle would jump around. By cleaning up the ground on the front wiring harness the needle stop jumping around. On a 5210, how the temperature works is: Temperature sender is a variable resistor that responds to changes in coolant temperature. Low coolant temperatures cause high resistance. High temperatures cause low resistance. Current attempts to flow back to ground from gauge. If resistance of sender is high (low temperatures), only a slight amount of current passes to ground. This results in little or no movement of the gauge needle. A low temperature reading results. If resistance of sender is low (high temperatures), current flows readily through sensor back to ground. Needle movement increases and the gauge displays a reading that corresponds with the warmer temperature. Sensor resistance between these two positions varies in proportion to changes in coolant temperature.
If your tractor is still under warranty, I would contact the dealer. The temperature sensor for your tractor is RE515494 and the cost is $37.75. It would appear from the parts catalog it is located on top near the front of the engine. Let痴 hope it is not the gauge as it appears the instrument cluster RE281263 would have to be replaced. Double check with the dealer, on the part numbers should you decide to replace anything.
Here is a link to the John Deere parts catalog.
jdpc.deere.com/jdpc/servlet/com.deere.u90490.partscatalog.view.servlets.HomePageServlet_Alt