Is the blower working? Could the heater core be "blown? If the controls are electronic, there could be a bad relay in them. It honestly sounds like a problem for the dealership will need to track down.
Upper and lower radiator, inlet and outlet heater core, bypass,Upper and lower radiator, inlet and outlet heater core, bypass,
Heater core? Inlet or outlet hose fitting at heater core?
Remove both heater hoses from inlet & outlet of heater core. Connect these hoses together.
Disconnect heater core inlet and outlet hoses - couple them together
Simple, take the inlet and outlet hoses going to and from the heater core and connect them together.
No it will not, it will just back flush the heater core and clean it out.
There are two heater core hose that goes to the firewall the inlet and outlet. through that hose, you will also have the rear heater core hose attached to a T joint in both the inlet and outlet hose. You splice the hose of the front heater core inlet and connect that to the rear heater core inlet hose. Same goes to the Outlet hose with the T joint using a conncetor which you can buy at your auto parts store, 3/4 inch size. Basically you are bypassing the front heater core that is connected to the firewall. You wont have any defroster and heater for the front, but the rear vents and control will have heat.
The outlet from the 350 engine to feed the heater core would be the one closest to the thermostat.
Couple inlet and outlet hoses together
The outlet from the engine that feeds hot coolant into the heater core is usually (but not always) located close to the thermostat. The return hose from the heater core usually returns into the water pump.
I don't know about the outside diameter of the hoses but, the outside diameter of the heater core inlet and outlet tubes are 3/4" (inlet) and 5/8" (outlet).
2 - inlet & outlet