We study the origin of photocurrent generated in doped multilayer BP photo-transistors, and find that it is dominated by thermally driven thermoelectric and bolometric processes. The experimentally observed photocurrent polarities are consistent with photo-thermal processes. The photo-thermoelectric current can be generated up to a $mu$m away from the contacts, indicating a long thermal decay length. With an applied source-drain bias, a photo-bolometric current is generated across the whole device, overwhelming the photo-thermoelectric contribution at a moderate bias. The photo-responsivity in the multilayer BP device is two orders of magnitude larger than that observed in graphene.