Hi,
It could be one or two things.
The outer casing of the cable can slip in its mounting at the control lever end,
and the lower inner cable fixing can also slip at the heater valve.
I suggest you compare the motion of the valve to the movement
of the dash lever.
The valve lever can be encouraged to rotate a little further in order to shut off the water flow.
You may be able to adjust the position of the cable at the valve so as to go fully closed
and partially open on hot, which would be a good compromise for your trip, and until
you have time to investigate further.
Nigel