[Blas]

Take the thermostat out of the car and see if the problem persists. As was mentioned earlier, installing the thermostat backwards or if there is an interference with its opening due to its design, it could also be faulty. Taking it out removes it from problem statement.
Thermostat should say "Engine Side" on it and should have a weep hole in the plate body, which should be orientated in the top position when installed. Drill on 1/8" hole if it does not have one.
If this is an option for your engine: Get a "Balanced Thermostat" designed thermostat. I believe they fail open.
If your temp switch is similar in design and operation to a SPF. (two wires in a plug on the radiator) just remove and attach the two wires together or jump them (they are just a ground switch) If you have a single wire sensor in a hose or radiator, it is also just a ground. Just disconnect and use a jumper wire to a new ground to activate fans. Don't know if your fans will run with ignition off. SPF's will. Take one component out of the equation to get fans running. Another thing to verify is direction fan or fans move air. Air should be moving "into" engine compartment.