Powder bed fusion (PBF) is an additive manufacturing (AM) process that builds parts in a layer-by-layer fashion out of a bed of metal powder via the selective melting action of a laser or electron beam heat source. Despite its transformational manufacturing capabilities, PBF is currently controlled in the open loop and there is significant demand to apply closed-loop process monitoring and control to the thermal management problem. This paper introduces a controls theoretic analysis of the controllability and observability of temperature states in PBF. The main contributions of the paper are proofs that certain configurations of PBF are classically controllable and observable, but that these configurations are not strongly structurally controllable and observable. These results are complemented by case studies, demonstrating the energy requirement of state estimation under various, industry relevant PBF configurations. These fundamental characterizations of controllability and observability provide a basis for realizing closed-loop PBF temperature estimation.