This contribution presents a new approach to control the local material properties of metal parts produced by wire-arc additive manufacturing (WAAM). During the WAAM process, deposited material experiences a sequence of thermal cycles which results in a particular microstructure. This microstructure is associated with certain material properties, e.g. for high-strength low-alloy (HSLA) steels, hardness and yield strength depend on the resulting various aspects of the microstructure such as grain size and morphology, texture and solid-state phase composition. In order to achieve the desired properties in a certain target location of a part, the thermal history of each material point therein must be shaped in the direction required to form the right microstructure. The local thermal history depends on the process parameters, environmental conditions and part geometry. We consider the scenario where the former are difficult to influence, and the main freedom to modify the thermal history is through changing the part geometry. We present a method based on topology optimization, to find part geometries that achieve the required thermal history in a target region, while maximizing part stiffness. This method involves a layer-by-layer transient thermal process simulation to predict temperature histories, based on which microstructure predictions and finally material property predictions are obtained. A significant computational challenge already exists to integrate the process simulation in topology optimization. Moreover, it is required to develop a new formulation to model the influence of the obtained thermal history on the material properties. To address this, we introduce a differentiable approach to determine the critical thermal cycle as well as the cooling time that determines the microstructure, which allows the use of gradient-based optimizers to perform the topology optimization. To our knowledge, this work constitutes the first example of part design for specific material properties, by exploiting the specifics of the WAAM process. The principle is expected to also apply to other AM processes where material properties depend on the thermal history during printing. Due to the high computational cost, 2D numerical examples for HSLA steel will be presented to illustrate the effectiveness and potential of the method.