Context. Numerical three-dimensional (3D) radiative (magneto-)hydrodynamical [(M)HD] simulations of solar convection are nowadays used to understand the physical properties of the solar photosphere and convective envelope, and, in particular, to determine the Sun's photospheric chemical abundances. To validate this approach, it is important to check that no excessive thermodynamic fluctuations arise as a consequence of the partially incomplete treatment of radiative transfer causing radiative damping that is too modest. Aims: We investigate the realism of the thermodynamics in recent state-of-the-art 3D convection simulations of the solar atmosphere carried out with the Stagger code. Methods: We compared the characteristic properties of several Fe i lines (557.6 nm, 630 nm, 1565 nm) and one Si i line at 1082.7 nm in solar disc-centre observations of different spatial resolution with spectra synthesized from 3D convection simulations. The observations were taken with ground-based (Echelle spectrograph, Göttingen Fabry-Pérot Interferometer (GFPI), POlarimetric LIttrow Spectrograph, Tenerife Infrared Polarimeter, all at the Vacuum Tower Telescope on Tenerife) and space-based instruments (Hinode/Spectropolarimeter). We degraded the synthetic spectra to the spatial resolution of the observations, based on the distribution of the continuum intensity Ic. We estimated the spectral degradation to be applied to the simulation results by comparing atlas spectra with averaged observed spectra. In addition to deriving a set of line parameters directly from the intensity profiles, we used the SIR (Stokes Inversion based on Response functions) code to invert the spectra. Results: The spatial degradation kernels yield a similar generic spatial stray-light contamination of about 30% for all instruments. The spectral stray light inside the different spectrometers is found to be between 2% and 20%. Most of the line parameters from the observational data are matched by the degraded HD simulation spectra. The inversions predict a macroturbulent velocity vmac below 10 m s-1 for the HD simulation spectra at full spatial resolution, whereas they yield vmac ≲ 1000 m s-1 at a spatial resolution of 0.″3. The temperature fluctuations in the inversion of the degraded HD simulation spectra do not exceed those from the observational data (of the order of 100-200 K rms for -2 ⪉ log τ500 nm ⪉ -0.5). The comparison of line parameters in spatially averaged profiles with the averaged values of line parameters in spatially resolved profiles indicates a significant change in (average) line properties on a spatial scale between 0.″13 and 0.″3. Conclusions: Up to a spatial resolution of 0.″3 (GFPI spectra), we find no indications of excessive thermodynamic fluctuations in the 3D HD simulation. To definitely confirm that simulations without spatial degradation contain fully realistic thermodynamic fluctuations requires observations at even higher spatial resolution (i.e. <0.″13). Appendices A and B are available in electronic form at http://www.aanda.org