It's not just BMW's, I had a warning on my wife's Caddy SRX a little while ago. The system showed 25 and 26 psi with the outside temp. at 14 degrees F. After city driving less than 2 miles the light went out and the sensors were already reading 28 and 29 psi.

I'll bump them up a couple of pounds.....this weekend when the temp. is back in the 40's!

 

I would say this. The minimum pressure when cold should always be as shown on the door sticker. If you set them to that in warm weather, they WILL be too low in winter and you should add a few PSI. It sounds like the TPM is correct in warning the lower pressure. You should add a few PSI and reset the TPM. There is probably no need to drop them after a 20 degree warm up but maybe so in a 40-50 degree warmup if it will likely stay that way. Charlotte had 75 degrees a few weeks ago and 19 this morning. That makes a several PSI difference.

If the pressures are bumped up in cold weather and there is a large swing in temp or you are extremely agressive driving, the tire temps will climb signicantly but should stay under max pressure, so no problem. On track in December, my left front Conti went from 36psi to 45psi in 35 degree weather. In the afternoon sun, I dropped the tires several PSI to keep them in the range I wanted.