Taylor,
A Baker Heater is a circulating hot water heating system. The hot water circulated through the car by convection through a pipe laid around the footboard and under the seats. The expansion tank for the system would usually be in a enclosed box on top of the side of the roof.
If you have access to a copy of "The American Railroad Passenger Car" by John H. White, there are several pages about hot water systems and the Baker system specifically. This book was published by Johns Hopkins University Press first as a 700-page hardbound book and later as a two volume softcover work. If you are working with, or interested in, railroad passenger cars, I would suggest you see about obtaining a copy.
Baker heaters generally went out of fashion when steam heating came into use. However, RR business cars often also had Baker systems because they would be carried at end of freight and mixed trains or set-out where steam heat was not available. Interesting is that the Great Northern bought lightweight passenger cars after WWII with auxiliary Baker heating systems.
Brian Norden