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I'm with Eagle on as you need to make sure that it is actually leaking or not.

You just might be doing what many (most) folks new to Model A's do is to overfill the radiator.

There is a lot of flow coming from the water pump into the top of the radiator when running at higher speeds. The coolant expands as it heats up and that combined with a high coolant level, the increase in flow and possibly the baffle being damaged, deteriorated or missing will cause water to push out of the overflow tube and also seek it way past a faulty or loose radiator cap gasket.

Drive your car and let it push the excess coolant out until it finds the level it is comfortable with. Just keep checking it to make sure that it stays above top of the tubes in the radiator. As long as it stays above the tubes you are fine as far as the coolant level is concerned.

You say that it got hot but not to the point of overheating. Do you know for sure what the temperature was? Do you have a gauge or a motor meter on the radiator cap? The motor meters get you in the general area on temp but by no means are spot on accurate.
I use a cheap dial meat thermometer that I place in the neck of the radiator directly into the coolant. You can open up the radiator at any time since it is not pressurized and check the temperature. You really need to know what the temperature is for sure if you suspect overheating. Frankly I think it it a good idea to check the temperature of any "new" A for a while to get a good feel for how it is behaving temperature wise.

If you do have a small leak in a seam or someplace that is easy to get to there is a simple fix that while may not be a permanent fix is a pretty darn long lasting fix. It also save's $$'s.

Cut a piece of cotton tee shirt type cloth just a bit bigger than the crack and saturate it with silicone gasket sealant and apply it over the failed area. Of course clean the area very well first. Using black cloth and black silicone will help keep it from being too noticeable.

I've done this type of repair to many different things and it works well. Did this to the radiator on my AA on a small leak in the area you are looking at just about 10 years ago and it is still fine.

Welcome to the hobby. Fun stuff this is.