We present time-resolved optical spectroscopy of the ‘redback’ binary millisecond pulsar system PSR¿J1023+0038 during both its radio pulsar (2009) and accretion disc states (2014 and 2016). We provide observational evidence for the companion star being heated during the disc state. We observe a spectral type change along the orbit, from ~G5 to ~F6 at the secondary star’s superior and inferior conjunction, respectively, and find that the corresponding irradiating luminosity can be powered by the high-energy accretion luminosity or the spin-down luminosity of the neutron star. We determine the secondary star’s radial velocity semi-amplitude from the metallic (primarily Fe and Ca) and Ha absorption lines during these different states. The metallic and Ha radial velocity semi-amplitude determined from the 2009 pulsar-state observations allows us to constrain the secondary star’s true radial velocity K2 = 276.3 ± 5.6 ¿km¿s-1 and the binary mass ratio q = 0.137 ± 0.003. By comparing the observed metallic and Ha absorption-line radial velocity semi-amplitudes with model predictions, we can explain the observed semi-amplitude changes during the pulsar state and during the pulsar/disc-state transition as being due to different amounts of heating and the presence of an accretion disc, respectively.