This study presents a Topology Optimization (TO) methodology for determining the optimal distribution of support structures in the powder bed fusion Additive Manufacturing (AM) fabrication technology. The support structures enhance thermal dissipation, reducing distortion on overhang surfaces during the build process and improving printability. A novel transient thermoelastic layer-by-layer model simulates the AM process, evaluating temperature and displacement in partially built structures with supports. We propose two new objective functions related to part distortion, perform their adjoint sensitivity analysis, and present a comprehensive set of numerical experiments with different geometries and levels of overhang complexity. The numerical results show non-standard optimal support structures obtained using the proposed TO-AM methodology for different model parameters, including support volume, thermal anisotropy, time discretization method, and building times for each layer.