It is most probably a broken heater core or a plastic ipe from the firewall to the heater core.
Don't panic.
First of all: does your car have aircon or only heater system?
If no aircon, very easy to change, if the system is Siemens.
http://www.bimmerboard.com/forums/posts/143292/
In case of aircon it becomes more complicated, but doable DIY, because the delaer will charge you an terrible amount for the hours.
In old times people removed the dash complete, that is no longer required.
This we have done in 4-6 hours
http://www.bimmerboard.com/forums/posts/427855/
and more
http://www.bimmerboard.com/forums/posts/328048
http://www.bimmerboard.com/forums/posts/454565/
http://www.bimmerboard.com/forums/posts/451343/
http://www.bimmerboard.com/forums/posts/327622/
temporary fix
Isolate cabin heater from engine cooling
http://www.bimmerboard.com/forums/posts/459398/
Just use the search on Bimmerboard E32 forum and type in heater core and you have enough info