2003 Hyundai Elantra thermostate is there a way to test it'

If you mean the coolant temp. Gauge in the car yes it can be inaccurate and if it is the most likely culprit is a faulty engine coolant temp (ECT) sensor. It's pretty obvious when an engine is overheating, you should be able to smell it, possibly see white smoke or wet spots, and the engine will be sluggish. The coolant may also be bubbling/gurgling in the overflow tank. All are signs of overheating.