It sounds to me as if the blender flaps in the air distribution box aren't working properly. They may have stuck in the cool position. I don't know the Qashqai system in any detail but most car heater systems work on air blending rather than water valve opening. The problem is that it probably needs half the fascia dismantled to access it and the dealer doesn't want the costs involved.
It may also be worth checking to see if the pollen filter is not blocked, but if you have good airflow from the vents then this is unlikely.
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