  Using non-equilibrium molecular dynamics simulations, it has been recently
demonstrated that water molecules align in response to an imposed temperature
gradient, resulting in an effective electric field. Here, we investigate how
thermally induced fields depend on the underlying treatment of long-ranged
interactions. For the short-ranged Wolf method and Ewald summation, we find the
peak strength of the field to range between $2 \times 10^7$ and $5 \times
10^7~\text{V/m}$ for a temperature gradient of $5.2~\text{K/}\unicode{x212B}$.
Our value for the Wolf method is therefore an order of magnitude lower than the
literature value [J. Chem. Phys. 139, 014504 (2013) and 143, 036101 (2015)]. We
show that this discrepancy can be traced back to the use of an incorrect kernel
in the calculation of the electrostatic field. More seriously, we find that the
Wolf method fails to predict correct molecular orientations, resulting in
dipole densities with opposite sign to those computed using Ewald summation. By
considering two different multipole expansions, we show that, for inhomogeneous
polarisations, the quadrupole contribution can be significant and even outweigh
the dipole contribution to the field. Finally, we propose a more accurate way
of calculating the electrostatic potential and the field. In particular, we
show that averaging the microscopic field analytically to obtain the
macroscopic Maxwell field reduces the error bars by up to an order of
magnitude. As a consequence, the simulation times required to reach a given
statistical accuracy decrease by up to two orders of magnitude.
