  Resolved maps of the thermal and nonthermal radio continuum (RC) emission of
distant galaxies are a powerful tool for understanding the role of the
interstellar medium (ISM) in the evolution of galaxies. We simulate the RC
surface brightness of present-day star forming galaxies in the past at
$0.15<z<3$ considering two cases of radio size evolution: (1)~no evolution, and
(2)~same evolution as in the optical. We aim to investigate the a)~structure of
the thermal and nonthermal emission on kpc scales, b)~evolution of the thermal
fraction and synchrotron spectrum at mid-radio frequencies ($\simeq$1-10\,GHz),
and c)~capability of the proposed SKA1-MID reference surveys in detecting the
RC emitting structures. The synchrotron spectrum flattens with $z$ causing
curvature in the observed mid-radio SEDs of galaxies at higher $z$. The
spectral index reported in recent observational studies agrees better with the
no size evolution scenario. In this case, the mean thermal fraction observed at
1.4\,GHz increases with redshift by more than 30\% from $z=0.15$ to $z=2$
because of the drop of the synchrotron emission at higher
rest-frame~frequencies. More massive galaxies have lower thermal fractions and
experience a faster flattening of the nonthermal spectrum. The proposed
SKA1-MID band~2 reference survey, unveils the ISM in M51- and NGC6946-like
galaxies (with ${\rm M_{\star}}\simeq10^{10}\,{\rm M}_{\odot}$) up to $z=3$.
This survey detects lower-mass galaxies like M33 (${\rm
M_{\star}}\simeq10^{9}\,{\rm M}_{\odot}$) only at low redshifts $z\lesssim
0.5$. For a proper separation of the RC emitting processes at the peak of star
formation, it is vital to include band~1 into the SKA1-MID reference surveys.
