my 1992 toyota paseo(automatic) has a probable thermostat problem?

[pelavacas]

Hi, I live in las vegas, and when I drive in the morning, my cars temperature gauge takes forever to go to the middle signalizing a warm engine, and its rpms stay at around 4rmps, then when temp finally goes up, the rpms go down to 2 1/2 and engine seems less forced, but the a few minutes later, the gauge shows its a cold engine and at same speed it revs 4thousand rpms. What could be the problem? I was reading online, and think its the thermostat, but which one, or which sensor? car has 120k miles, all stock, original thermostat too