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Welcome, I'm Chris (aka Moose), my normal schedule online is around lunch and after dinner till early morning.
Is the concern you can not get any heat inside the vehicle?
Since the heater core flows when flushed forward and backwards but only one hose gets hot this indicates the concern is under the hood with a restriction on one of the heater core hoses or outlets or the water pump is not moving enough coolant or the thermostat is stuck open or there is air in the cooling system.
Please read this:
Thanks for using Just Answer, Chris
Hello again Chris here,