Gauges should swing left so they rest on Empty and Cold with key in off position. Are the gauges correct for a 57 Thunderbird or has someone replaced them?
I am thinking you might have a ground issue but don't understand the temp gauge parking on Hot.
Do you have a ground strap from the back of the engine to the firewall???? Originally on the driver's side head attached by a bolt rearward of the temp sender. Doesn't matter where it is really, just as effective any place as long as you have one.
Has any other wiring been changed?
What modifications do you have to the car?
Do you still have the generator or has an alternator been added?