We investigate the far-infrared–radio correlation (FRC) of stellar-mass-selected galaxies in the Extended Chandra Deep Field-South using far-infrared (FIR) imaging from Spitzer and radio imaging from the Very Large Array and Giant Metre-Wave Radio Telescope. We stack in redshift bins to probe galaxies below the noise and confusion limits. Radio fluxes are K-corrected using observed flux ratios, leading to tentative evidence for an evolution in spectral index. We compare spectral energy distribution (SED) templates of local galaxies for K-correcting FIR fluxes and show that the data are best fitted by a quiescent spiral template (M51) rather than a warm starburst (M82) or ultra-luminous infrared galaxy (Arp 220), implying a predominance of cold dust in massive galaxies at high redshift. In contrast, we measure total infrared luminosities that are consistent with high star-formation rates. We observe that the FRC index (q) does not evolve significantly over z= 0–2 when computed from K-corrected 24- or 160-μm photometry, but that using 70-μm fluxes leads to an apparent decline in q beyond z∼ 1. This suggests some change in the SED at high redshift, either a steepening of the spectrum at rest-frame ∼25–35 μm or a deficiency at ∼70 μm leading to a drop in the total infrared–radio ratios. We compare our results to other work in the literature and find synergies with recent findings on the high-redshift FRC, high specific star formation rates of massive galaxies and the cold dust temperatures in these galaxies.