Aye it does totally sound like the clutch pack is burnt out, slipping when hot, burnt smelling fluid, is it also a dark brown colour on a white tissue, instead of a pinky-red? I would say the box has had it mate, sorry but maybe a second hand box would be much cheaper than any rebuild. Your TC should have lasted more than 30k, any chance the fitting garage would consider a warranty claim on them? Just a thought.
Big lump of metal to man-handle the auto-box, not a roadside job really, needs a 4 poster ramp a transmission lifter and 2 men to fit one.
A fluid drain and refill isn't that hard, though you still need a ramp to lift it for good access to the drain plug and pan. If the oil wasn't done or the old stuff was reused (hard to believe, but happens when monkeys use spanners) then it could be very burned fluid if you are lucky, and may just scrape it with a drain and refill PLUS filters as they will definitely need done if the oil is burned and the clutches are going. It might not work, but cheap enough to be worth a try.
The fact it drives when cold may just be your saving grace. If the clutch pack was totally shagged now it wouldnt pull away without loads of revs and slip and drama even cold. A siezed TC would be a dog and sluggish as hell to pull away but not so revvy.
If it drives fine cold, try a fluid and filter change first.