Slow transmission shift after cold soak

When I lived in Connecticut- a 1973 V-8 LTD Ford, with 90000 miles would not shift in the winter after being outside over night until the engine warmed up somewhat. I finally had it towed and I believe the pan was dropped and some parts changed to fix the problem.( Someone called it morning sickness.)

Now I live in Florida , but when I take my 2001 V6 LeSabre (>100000 miles) to Connecticut in the winter, I must warm up the engine, after a nght cold-soak before the transmission will shift into gear.

I’ve contacted Buick dealers in FLorida and Connecticut and was told they can’t give me an estimate because they’ve never heard of this? Can it be fixed without changing transmissions? WIll it eventually not shift at all after a cold-soak ? I’d appreciate any insight into this phenomenon. Thanks Bob