If the cable had come off it would not be stiff - it just wouldn't do anything.
Like Redwood says, it is probably the cable with a bit of rust in it, fairly easily fixable once you get to it.
Otherwise it might be the heater valve. They do go bad and are fairly expensive to replace.
There are other options though - Napa has a non-thermostatic valve that can be adapted.
Could you post the last several digits of your VIN?
Mine is 008731.
--
George Downs, Bartlesville, Heart of the USA!

The dash doesn't have to come out, but removal of the lower dash panel makes it easier to access and work on.
I would also check the operation of the heater control valve for smoothness of operation.
You may get lucky and just have to re-clamp the cable at either end. I never get that lucky though, it's usually a problem somewhere.
--
'60 PV544, '68 220, '70 145, '86 745T

I would also check the condition of your heater valve on the engine side of the firewall, where the cable comes through. My dial also appeared frozen, but was still connected via the cable. Ended up being a heater valve that was so corroded and rusty that it had frozen in place.

No the dash doesn't have to come out.
It is a stiff wire and cable housing set up with a loop in the end of the wire that hooks around the control.
You can get a cable housing injector clamp at a motorcycle shop in your favorite color Kawasaki green or Honda red. Then tri flow or LPS 3 with the straw will clean and lube the cable housing.
--
71-145-S