There could be an issue with a blend door that directs airflow over the heater core. Did you replace the core because it was leaking and did you have heat before all this?
Alex
BOTH heater hoses should be as HOT as the top radiator hose is when engine is at *normal* operating temperature .. Should not be able to grasp heater hoses without it quickly becoming uncomfortable.
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No heat stopped working so new heater core was put in when radiator was done