The investigation of the behaviour of water under thermal fields is important to understand thermoelectricity of solutions, aqueous suspensions, bioelectric effects or the properties of wet materials under spatially inhomogeneous temperature conditions. Here we discuss the response of bulk water to external thermal fields using non-equilibrium molecular dynamics simulations, and five widely used forcefields: TIP4P/2005, TIP4P/2005f, OPC, SPC/E and TIP3P. These models all show the thermal polarisation (TP) effect in bulk water, namely the build-up of an electrostatic field induced by the temperature gradient. The strength of this effect is ∼0.1-1 mV K-1 at near-standard conditions for all forcefields, supporting the generality of TP. Moreover, all the models predict a temperature inversion of the polarisation field, although the inversion temperatures vary significantly across different models. We rationalise this result by deriving theoretical equations that describe the temperature inversion as a balance of the isobaric thermal expansion, dipole orientation in the thermal field and the ratio of the molecular dipole/quadrupole moments. Lower ratios lead to higher inversion temperatures. Based on our results, we conclude that the accuracy of the forcefields describing the TP effect decreases as, TIP4P/2005 ∼ TIP4P/2005f ∼ OPC > SPC/E > TIP3P. At coexistence conditions, the inversion temperature is expected to be around 400 K. Furthermore, we establish a correlation between the TP inversion temperature and the temperature corresponding to the minimum of the liquid-vapour surface potential of water.