I realized I made a mistake: A quick Google search reveals that air gets heated up to full body temperature in the lungs while the nasal turbinates, after inhal

I realized I made a mistake: A quick Google search reveals that air gets heated up to full body temperature in the lungs while the nasal turbinates, after inhalation, remain below body temperature for a bit longer. So upon breathing out T_N < T_A and heat indeed gets transferred back from the air to the nose.