You've just solved global warming. Just hook your cooling system up to the planet.
So, in theory, the T'stat stays shut until it reaches opening temperature. Normally, you see this as the temp rises and then drops, as a slug of cold water from the radiator enters the engine. the temp stabilizes as the thermostat and temperature of water exiting the radiator find a happy median. If you have excessively cold water exiting the radiator, then by the time it flows through the engine and gets ready to exit by the thermostat, it cools the engine too much, and the thermostat throttles down the flow until it warms up. If it never gets up to temperature, then the thermostat isn't closing properly, or the coolant is finding some other path through the radiator.
Are you confident that the temperature sensor is accurate? Have you verified it by some other means? Does the radiator get hot?
As far as the A/C goes, it's normal for it to engage at any defrost setting, as it also de-humidifies the air, making it good to defog windows.
Does the heat not work as well? I would also check for proper operation of the fan clutch.