My car used to do the same as such but would probaly take a bit longer to blow cold.
after a while of head scratching a mechanic friend of mine noticed the rubber pipe from the metal pipe attached to engine going to the heater matrix (hope that made sense) was kinked, it should have a bend anyway but not like this was, ?6 from vag and it seems to have been cured,
Definately worth a look at
1990 8v gti