The accretion flow around the Galactic Centre black hole Sagittarius A* (Sgr A*) is expected to have an electron temperature that is distinct from the ion temperature, due to weak Coulomb coupling in the low-density plasma. We present four two-temperature general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of Sgr A* performed with the code KORAL. These simulations use different electron heating prescriptions, motivated by different models of the underlying plasma microphysics. We compare the Landau-damped turbulent cascade model used in a previous work with a new prescription we introduce based on the results of particle-in-cell simulations of magnetic reconnection. With the turbulent heating model, electrons are preferentially heated in the polar outflow, whereas with the reconnection model electrons are heated by nearly the same fraction everywhere in the accretion flow. The spectra of the two models are similar around the submillimetre synchrotron peak, but the models heated by magnetic reconnection produce variability more consistent with the level observed from Sgr A*. All models produce 230 GHz images with distinct black hole shadows which are consistent with the image size measured by the Event Horizon Telescope, but only the turbulent heating produces an anisotropic `disc-jet' structure where the image is dominated by a polar outflow or jet at frequencies below the synchrotron peak. None of our models can reproduce the observed radio spectral slope, the large near-infrared and X-ray flares, or the near-infrared spectral index, all of which suggest non-thermal electrons are needed to fully explain the emission from Sgr A*.
