Wondering if any one can help. I have a one owner Buick Rivera with 338,000miles (daily driver). The motor has never been opened and the serve maintenance schedule has been followed since day one. The cooling system was original but has been completely replaced all but the heater core has been replaced. With exception of the heater core which has been flushed and found to be running freely and clearly. The coolant was flushed yearly since new. The block was pressure tested and coolant tested for signs of combustion chemicals in the fluid and the test came back negative. There is also no coolant in the oil. The cooling system does hold vacuum without any issue. The lower heater hose runs at temperature and the top hose is cold. The heater blend door has been checked and is working perfectly and is adjusted properly. I am stuck at this point am left with replacing the heater core next. Any suggestion or advise would be greatly appreciated.

Sounds like the core itself is clogged. If one hose is warm/hot and the other is still cold, then you have a flow issue. Unless you have a cable driven shutoff that controls the temperature and it broke somehow.

Wow! Excellent!

Shouldn't be the core based on this.
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I was thinking of a heater coolant valve too. Perhaps when flushed it was just the heater core, and now while mmurphy is testing, it is with a not-operative valve inline. In the 70'*, Buick (and probably more of GM) had vacuum-operated heater coolant control valves. It might be the valve itself, or a vacuum issue facing it. For reference, the valve I'm talking about looks like this:



The cable-operated units like Mike mentioned look similar except they usually don't have a 90-degrees direction change, no diaphram, and a place to mount a cable housing (like the brakes on many bicycles except more rugged) . I think your car is fairly electronicallized so it probably has a vacuum operated one if it has one at all.