In dismantling the heater / air conditioning assembly I notice a capillary tube running from the heater flow valve into and along the heater core; the tube is sealed and does not connect to the core.
What is the function of this feedback?
Shouldn't be any capillary tube coming off the heater tap, more likely you are looking at the valve that controls the gas flow in the air conditioning. It has a line which senses the temperature in the evaporator, and is supposed to do two things - stop the evaporator from icing up or freezing, and ensure that no liquid is returned to the compressor (as a liquid is incompressible).
J&H,
I do have airconditioning and as you indicated there is the mandatory aluminium capillary tube to the evaporator.
The capillary tube in question is made of copper and is attached to the top part of the heater valve, just below where the actuating lever comes in contact with the plunger; at the heater core end it is crimped closed while at the valve end it is braze into a hole drilled into upper part of the pluger.