Heat failure

have replaced thermostat and flushed radiator on 1999 sable wagon but no heat,mechanic wants to replace heatercore, hesitant to follow his suggestion hes not sure whats purpose of second hose help

Heater cores have two hoses; one is the input to the core the other is a return to the block. If your mechanic does not this, I would be moving on to another mechanic fast.

When you refilled the radiator, was the heater turned on so as when you filled the system, it would also fill the heater core.

If I am correct, when the heat is selected, a valve is opened so that hot water will flow through the core. I could not tell you where that valve is, but I believe that one of the first things to check.

Your mechanic probably has the right idea. If a new thermostat won’t give you heat, and the temperature gauge reads normal, then you likely have a blocked heater core. Of course you ought to test this idea first. Remove the outlet hose and see if there’s a flow. If the flow is present but weak, try a power flush of the core. If all else fails, you need a replacement.

If the second hose is the bypass hose, the purpose of said hose is to maintain coolant flow in the event the heater core gets clogged. Its doing its job. Do not eliminate it! You may try flushing the heater core by disconnecting the heater hose at the thermostat housing, and the heater hose at the water pump, crimp the bypass hose and run full garden hose water pressure through the heater core. Note, properly drain coolant first, and this assumes the engine is the Vulcan.

If both hoses to and from the heater core are hot then you may have a blend door problem. The blend door is what shuts off airflow through the heater core when heat is not needed.

If your car has EATC (elec. air temp controls) then a problem could possibly be diagnosed by allowing the unit to perform a diagnosis.
If your car has this feature you can run the diagnostic by pressing the OFF and FLOOR buttons at the same time. Let up and quickly press the AUTOMATIC button.
This will be followed by 20 or 30 seconds of gibberish.
If you get a Code 25 this means a blend door malfunction.
If your car does not have EATC then skip this paragraph. Hope that helps.