Whether or not anomalies in the thermal conductivity from insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $kappa$ and specific heat $c_v$ of the half-filled 2D single-band Hubbard model using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. Both $c_v$ and $kappa$ possess two peaks as a function of temperature, with scales related to the Hubbard interaction energy $U$ and spin superexchange energy $J$, respectively. At low temperatures where the charge degrees of freedom are gapped-out, our results for the contribution to both $c_v$ and the Drude weight associated with $kappa$ from the kinetic energy agree well with spin-wave theory for the spin-$frac{1}{2}$ antiferromagnetic Heisenberg model.
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