I have a 2000 BMW 528i. The speedometer works when its cold then it turns off as I am driving. What could it be?

There is a censor on diff casing the connection needs to checked as it gets deteriated with dirt and spray from roads

Take it out while cold and place in hot water, if it's working you will see it open up visually

pull plugs and marvel mistery oil in all holes let sit 24 hours then try to turn over buy hand if that dose not work pull oil pan and losen all rod and crank bolts if that dose not work tare it down and see whats wrong

Have your thermostat checked, sound like it is not working when cold.

You can find the procedure here
https://resetoillight.com/bmw/oil-change-light-reset-bmw-528i-1998-1999-2000/

The wiper relay is a common cause of this failure. It is not very expensive and easy to replace. Search Google to find a replacement and instructions. Use these terms: e39 wiper relay

mostly these happen when your suspesion is gone, get your car checked the suspension need attetion

Click on the following Link. It has the Diagram's and Photo's you need to Remove and Replace your Serpentine Belt, including the procedure in loosening the Tensioner.
http://www.2carpros.com/car_repair_information/year/2000/make/bmw/model/528i/2000_bmw_528i_drive_belt_routing_diagram.htm

There be one on each of your rear drive wheels.
If the speedometer and odometer do not work, the driver's side rear sensor is probably bad. If the speedometer works but the cruise control does not, then the passenger side rear sensor is probably bad.