Ice Pack,
Methinks your garage are" taking the michael" - The wire goes from the dash control knob down to a arm at the LHside of the heater box the wire is inside a cable outer and if you can drip some light oildown the wire inside the outer, the wire will move much more easily -- also greasing the arm at the heater box end also works wonders as does a spray of WD 40 or spray grease on the control arm shaft into the heater box - as JMc says!!
It should not take a competent mechanic more that 10 - 20 Minutes
Cheers!