Coolant discharge from over fill tube...
 

On my 55 Super 88, I've noticed that coolant is leaking from the discharge tube on the rad after 5 or 10 minutes of running. I have also noticed that the temperature gauge is not showing any temperature change. Could this indicate that the thermostat needs to be replaced ? I'm thinking that this might be problem and I should just go and replace it.

Discharge from the overflow tube is not -necessarily- indicative of a problem. The coolant expands when hot and will be expelled if the expanded level is above the discharge tube opening. Theoretically, it should correct itself after a few discharges.

Did you recently fill/top off the radiator?
Does it overflow every time?
What does "the temp gauge is not showing any change" mean?
Is it staying within the normal range?
Is it not registering anything at all?
Have you checked the seal on the radiator cap?
Is it the correct cap for the car in terms of lbs of pressure?

Thanks for your questions Dave. No, The rad was not filled recently. I've only had the car two weeks , and I did not notice it leaking when my son and I went to look at and test drive the car. We noticed the overflow when it was sitting in my driveway while we were going over the car. The temp gauge shows no movement from the resting position. When driving it stays in the same spot not registering anything. I'm going to change the temp sensor and the thermostat so I might replace the cap just to be on the safe side.