Shift problem in cold weather

Re my 1997 Thunderbird with 52,000 miles: For the past 2 months or so, in cold Berkeley, CA, weather I have been unable to shift from Park to Drive until the car heats up, in 4 minutes or so. This never occurred previously and I have the oil changed and car checked every three months. I wonder if it can be related to the COLD (about 40-48 degrees) or perhaps moisture from WATER, for my terrier in the cup holder, (water,not my dog, in the holder) spills over when he drinks onto the shift handle. Any thoughts? Apart from this the car runs fine. Thanks to all.

I’d probably check the brake interlock solenoid. It may be sticking at cooler temps.