Diagnosis
The thermostat sensor is failing or has poor contact with the plate. It can't maintain setpoint under load.
How to Fix It
Unplug. Remove the two hinge screws and top plate. Locate the small white thermistor pressed against the plate. Clean its contact point with isopropyl alcohol. Reassemble ensuring it's snug against the metal.
If That Didn't Work
The thermistor itself is faulty. Its resistance values drift. This requires main board replacement, as it's integrated.
Heads Up
Do not try to adjust the thermostat calibration. You will cause overheating and damage the plates or your hair.