Could thermostat that's stuck open make a squeaky noise under the hood(read details) 10 points for best answer?

Thermostat's have only to do with the exchange of water from the engine to the radiator, not related to a squeak at all. The squeak will be the result of a pulley bearing or a loose belt. Best way to locate the problematic area is to take a stick, similar to a broom handle and use it like a stethoscope with the engine running, and during the symptom, careful not to get caught up in a belt. All pulleys have bearings, bad bearings may cause a drag on the pulley. The belt may be having a difficult time driving the pulley. You may also have not enough tension on the belt itself. Try the stethoscope, it works.