  We use quantum kinetic theory to calculate the thermoelectric transport
properties of the 2D single band Fermi-Hubbard model in the weak coupling
limit. For generic filling, we find that the high-temperature limiting
behaviors of the electrical ($\sim T$) and thermal ($\sim T^2$) resistivities
persist down to temperatures of order the hopping matrix element $T\sim t$,
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 $5\pi^2/36$.
