I did a post on this several years ago. So far back, that I can't remember much about it... . but then, I spend several hours a day looking for stufff around the house.
However, I worked from the glove box side and I think I connected the old cable end with some nylon cord. Pulled that all the way through and then used the cord to pull the new cable end over to the heater control. For some reason it seemed that it would go easier this way, and it did do ok.
If I could do it again, I'd put some liquid graphite down the cable sleeve before installation.