It sounds to me like the transmission is excessisvely worn.

If I understand the problem correctly, after a warm-up period, the car will no longer stay in higher gears. Even a small amount of pedal pressure causes it to downshift.

This is most likely a driveability symptom of worn bands inside an automatic transmission. Many reputable transmission shops will diagnose for free; just be sure they don't disassemble anything to do it or you will have to pay the full cost to replace it.

If it's really an AW-71, you can find a used one at a junkyard for a couple hundred bucks and replace it with a friend. That's what I'd do, if the diagnosis is confirmed.

As others have suggested, you might consider having the fluid flushed. Simply draining and refilling it won't do; you need to hook up a machine and do it right. This should cost between $60-80 depending on where you live.

I hope this helps. If not, you might consider giving us more of an idea of the problem --- how long does it take before it starts to happen? Also, double- or triple-check the trans model number.

As a side note, since it seems to be temperature-dependant, it's probably not the kickdown cable adjustment.

If anyone doesn't understand any of the terms in this response, you can search the board or the FAQ for them.