Radiator keeps pushing fluid out

My radiator is original. I have a hard time keeping fluid in it, I have tried not to over fill it, keeping fluid level about one inch below cap. Put a new 14 pound cap on it, still wants to empty the radiator out, especially when I get heavy on the throttle.

Should I look at changing temp on thermostat? Should I warm up car more ?

Would a radiator flush help?

 

68 GT350, 302 engine. Have not pressure checked the system. We did put new hoses on it, all the fluid is blowing out of the radiator hose that comes off the top of the radiator at the top of the radiator at the cap.

 

Follow up. Took radiator off, it was clean as a whistle per the radiator shop.
Put on a fluid over flow container like you guys suggested. The engine pumped out about a gallon of fluid the first day. So I refilled the radiator and put fluid in the container, filling it half way. Seems to work. Will follow up.

 

Well heres the story of my radiator leak.

The radiator was clear, changed caps, added the overflow/collector tank, put block sealer in it. The car still lost half a gallon of fluid in about every time I got the revs up.

Had the guys at RATS pull off the heads. There were small leaks in the head gaskets and the engine block on top of the pistons was not smooth.

So they yanked out the engine and we are going to get the head smoothed out and a really good head gasket.

Will let you know the outcome, all of your input has been appropriate and led me in the right direction.

One of the spark plugs had evidence of water on it, we never did see any water in the oil.

This engine is the original, the head gasket appears to have been changed sometime previously.

 

I have put about every darn thing I can do into this car, Aluminum heads may be the next step.

Final result on my radiator pushing fluid out:
Anyway, the leak is gone. It was warped engine block heads and leaky gasket. I can now run car hard and at high rpm and the radiator fluid is staying in.