The truck already has a coolant shut-off valve attached to one of the heater core pipes behind the dash.........circled in red is the lever that the temp. selector mechanism pulls via a cable.....
If your temp. selector mechanism is broken, it may not be pulling & pushing the heater coolant shut-off valve all the way through it's range of motion, thus leaving it opened some when you have the dash temp. selector turned all the way to the cold (blue) side. It is very common for the plastic housing on that selector mechanism to break, and therefore limit it's range of motion. To check it, just get down on the driver's side floor and look toward the passenger side and just above the gas pedal......you should see the area in the pic above and then locate the cable that connects to the shut-off lever......while watching the lever, turn the temp. selector knob on the dash.......does that cable pull & push the lever a fair amount? You can turn the selector knob all the way to the cold side, and then push or pull (can't remember which way, but you will know once you see it!) the lever near the gas pedal to see if it can be moved any more. If it can, then your temp. selector housing (behind the knob on the dash) is more than likely broken.
Don't let the "clicking" as you rotate the knob fool you! It will still "SOUND" as if it is doing it's job, but it won't push & pull the cable to the shut-off valve as it should!!
Here is one that I changed out of my 1991 B2600i.......looks good doesn't it?
Uh.....NO!
A close-up of the area where the lever is at by the gas pedal....