Auto won't change when cold

[ph%wn.bbc@nr-comms.radio.bbc.co.uk (Heneghan,Paul)]

My 1982 Audi 100 Avant doesn't want to change out of 1st gear for the 
 first half mile or so when it's cold.  This problem becomes especially 
 noticeable the day after I've done a long run like 200 miles at 70mph.

What is causing this?
How much will it cost to get fixed?
Can I do it myself? (I've never opened a gearbox before, but I'm happy 
 to work on things like brakes, suspension, fuel system etc)

Paul

1984 Audi 80 quattro (135k)
1983 Audi 100 Avant (130k)