May be you have no stat fitted .Have you had the car long ,do you now if it as one fitted?.If you dont have one in i would say it was taken out because its running hot for some reason thus the cool running . It is an easy job removing the stat Some thermostat tops have an O ring around inner face and no paper gasket..

There is a stat. About a decade. It used to have a very consistent warm up pattern. You could see the response on the temp needle as if the stat was snapping open once warmed up.