We use quantum kinetic theory to calculate the thermoelectric transport properties of the two-dimensional single-band Fermi-Hubbard model in the weak coupling limit. For generic filling, we find that the high-temperature limiting behaviors of the electrical (∼T) and thermal (∼T2) resistivities persist down to temperatures of order the hopping matrix element T∼t, almost an order of magnitude below the bandwidth. At half filling, perfect nesting leads to anomalous low-temperature scattering and nearly T-linear electrical resistivity at all temperatures. We hypothesize that the T-linear resistivity observed in recent cold atom experiments is continuously connected to this weak coupling physics and suggest avenues for experimental verification. We find a number of other novel thermoelectric results, such as a low-temperature Wiedemann-Franz law with Lorenz coefficient 5π2/36. © 2021 American Physical Society.