Am I right to assume that the engine is using coolant and not pushing it out?
If that's the case then the radiator and cap can't be suspect because you would either see a leak from the radiator or the coolant reserve tank will be overflowing. And we can rule out a leak from the heater core because you would really smell coolant in the ventilation system.
There's all kinds of tests that can detect if combustion gasses are in the coolant, but they all rely on detection of hydrocarbons (in combustion gases) so that brings us to head gasket as the most obvious suspect and a crack in the head round the combuston chamber or exhaust port as the second.
An engine can still run nice and smooth in the early stages of a head gasket leaking.
Even it's confirmed that the head is the culprit you need to check the rest of the car.
Seeing as it's an automatic, still check that coolant is not escaping into the trans oil cooler that lives in the radiator (I've seen this especially on Saabs)
and also check the engine oil for contamination, the oil on the dipstick should look, well, oily, and not have any kind of milky discoloration, likewise another spot to look is the oil filler cap, if it has the 'coffee cream' look on the inside.
As for causes, these things happen because of:
- Overheating due to faulty thermostat/blocked radiator/ non working thermo fan/aircon assist fan or combination of them.
Corrosion
to poor servicing in the past or someone could have combined incompatible coolants at one stage and if that's happened the coolant becomes almost like acid and will eat things out from the inside. starting with the head gasket.
Check all these things out as well as....
If the top tank of the radiator is not shiny black and has any discolouration in the plastic it's a sure sign of continual hot running but rule of thumb, if a modern plastic/aluminium radiator is coming up to 10 years old I will be suspicious of it lasting much longer and I usually just replace it as a precaution. Some brands are better than others but the 10 years is about the average.
I didn't mention the water pump and as long as it's not noisy it is OK but.. if the car is apart for a fair while then the seal at the water pump bearing risks drying out and maybe leaking later on, which can be a real pain on a car like that.
see how you go, these are the logical steps but it's important to check them all out