Additive manufacturing (AM) is a manufacturing technique that adds material, such as polymers, ceramics, and metals, in patterned layers to build three-dimensional parts for applications related to medicine, aviation, and energy. AM processes for metals like selective laser melting (SLM) hold the unique advantage of fabricating metal parts with complex architectures that cannot be produced by conventional manufacturing techniques. Thermal transport can be a focal point of unique AM products and is likewise important to metal AM processes. This dissertation investigates AM metal meshes with spatially varied thermal conductivities that can be used to maximize the charge and discharge rates for thermal energy storage and thermal management by phase change materials (PCMs). Further, manufacturing these meshes demands excellent thermal control in the metal powder bed for SLM processes. Since the thermal conductivities of metal powders specific to AM were previously unknown, we made pioneering measurements of such powders as a function of gas infiltration. In the past, thermal transport was improved in phase change materials for energy storage by adding spatially homogeneous metal foams or particles into PCMs to create composites with uniformly-enhanced (UE) thermal conductivity. Spatial variation can now be realized due to the emergence of metal AM processes whereby graded AM meshes are inserted into PCMs to create PCM composites with spatially-enhanced (SE) thermal conductivity. As yet, there have been no studies on what kind of spatial variation in thermal conductivity can further improve charge and discharge rates of the PCM. Making such mesh structures, which exhibit unsupported overhangs that limit heat dissipation pathways during SLM processes, demands understanding of heat diffusion within the surrounding powder bed. This inevitably relies on the precise knowledge of the thermal conductivity of AM metal powders. Currently, no measurements of thermal conductivity of AM powders have been made for the SLM process. In chapter 2 and 3, we pioneer and optimize the spatial variation of metal meshes to maximize charge and discharge rates in PCMs. Chapter 2 defines and analytically determines an enhancement ratio of charge rates using spatially-linear thermal conductivities in Cartesian and cylindrical coordinates with a focus on thermal energy storage. Chapter 3 further generalizes thermal conductivity as a polynomial function in space and numerically optimizes the enhancement ratio in spherical coordinates with a focus on thermal management of electronics. Both of our studies find that higher thermal conductivities of SE composites near to the heat source outperform those of UE composites. For selected spherical systems, the enhancement ratio reaches more than 800% relative to existing uniform foams. In chapter 4, the thermal conductivities of five metal powders for the SLM process were measured using the transient hot wire method. These measurements were conducted with three infiltrating gases (He, N2, and Ar) within a temperature range of 295-470 K and a gas pressure range of 1.4-101 kPa. Our measurements indicate that the pressure and the composition of the gas have a significant influence on the effective thermal conductivity of the powder. We find that infiltration with He provides more than 300% enhancement in powder thermal conductivity, relative to conventional infiltrating gases N2 and Ar. We anticipate that this use of He will result in better thermal control of the powder bed and thus will improve surface quality in overhanging structures.