Troubleshooting help with a coolant thermostat problem. P0128 code. on 2002 Lexus ES300

The check engine light used to go off and on periodically. A month ago it came on and has not gone off. the code reads P0128, a coolant thermostat problem present. However, the engine temp gauge on my dash has been working perfectly normal this whole time. I am guessing it is a faulty sensor since, like I said, the check engine light used to go on and off periodically. What troubleshooting things can I do to find the solution?

Asked by for the 2002 Lexus ES300
Monitor the readings for coolant temp. sensor (for PCM-NOT fan) WITH scanner(live data) and see if it's opening to soon. Car may not be warming up fast enough for OBDII specs , and setting the code. Has t-stat ever been changed (with Toyota/Lexus part)?
Is there a cheap way to monitor the coolant temperature? I don't have a scanner. I would consider buying one if I needed to however. It is my wife's car and she doesn't think the thermostat has ever been replaced. She inherited the car maybe 5 years ago.
P0128 is indicating the engine is not warming up fast enough (simply put) , I would try replacing the thermostat first , I would also recommend getting the thermostat from the dealer. YES , it will seem outrageous compared to aftermarket , but 1) you know you're getting the right one , 2) the original lasted 12 years. Also factory coolant. IF you are saving the labor $$ by doing it yourself , get the best parts!