We use morphological descriptors, Betti numbers and Contour Minkowski Tensor
(CMT) on 21cm brightness temperature excursion sets, to study the ionization
and heating history of the intergalactic medium (IGM) during and before the
Epoch of Reionization (EoR). The ratio of eigenvalues of the CMT denoted by
$\beta$, gives shape information while it's trace gives the contour length of
holes and connected regions. We simulate the matter density, neutral hydrogen
fraction, spin temperature and brightness temperature field using the publicly
available code 21cmFAST in a redshift range of $z=20.22$ to $z=6$. We study the
redshift evolution of three quantities - the Betti number counts
$N_con,hole$, the characteristic size $r^ch_con,hole$ and shape
anisotropy parameter $\beta^ch_con,hole$ of connected regions and holes for
these fields and investigate the different physical origins of their evolution.
We make a qualitative comparison of different models of heating and ionization
during the EoR. We obtain different regimes of morphological evolution of
brightness temperature, depending upon how the shapes and sizes of connected
regions and holes change with redshift for different astrophysical settings
affecting the ionization and heating history of the IGM during and before the
EoR. We find that the morphology of the brightness temperature field traces the
morphology of ionized regions below a certain redshift value depending upon the
model, where $\Delta r^ch_hole<10 \%$ and $\Delta \beta^ch_hole<1 \%$
relative to the $x_HI$ field. This difference decreases with redshift.
Therefore, the ionization history of the IGM can be reconstructed using the
morphological description of $T_b$ in real space.