Heater blowing cold air please help

Hello all, brand new to the site, just bought my first jimny and I have to say I love the thing. Just one problem, when I was driving it home I decided to turn on the heaters and to my surprise the fan worked but it only blew cold air, I've trawled the net and here's what I've checked.
The cable and the white arm are still connected down by the clutch pedal.
There are no leaks anywhere.
Both pipes are hot coming through the bulk head to the matrix.
If I put my hand on the matrix from the driver side footwell I can feel heat.
For some reason I think it's something to do with the white arm that the heat cable connects to, i took the white arm off and turned the shaft by hand and it doesn't feel like its doing anything, it's really lose. Does the cable open and close a flap for hot and cold ???.
Sorry for long text any help appreciated.

Sounds like the spindle the white arm attaches too its not operating the internal flap.

That's what I was thinking, do I have to take out the whole matrix to try fix it. Thanks for the reply