  We carry out a thermal energy census of hot baryons at $z < 1$, by
cross-correlating the \emph{Planck} MILCA y-map with 0.8 million
clusters/groups selected from the Yang et.al (2021) catalog. The thermal
Sunyaev-Zel'dovich (tSZ) effect around these clusters/groups are reliably
obtained, which enables us to make our model constraints based on one-halo (1h)
and two-halo (2h) contributions, respectively. (1) The total measurement S/N of
the one-halo term is 63. We constrain the $Y$-$M$ relation over the halo mass
range of $10^{13}$-$10^{15} M_\odot/h$, and find $Y\propto M^{\alpha}$ with
$\alpha= 1.8$ at $z=0.14$ ($\alpha=2.1$ at $z=0.75$). The total thermal energy
of gas bound to clusters/groups increases from $0.1\ \rm meV/cm^3$ at $z=0.14$
to $0.22\ \rm meV/cm^3$ at $z=0.75$. (2) The two-halo term is used to constrain
the bias-weighted electron pressure $\langle b_yP_e \rangle$. We find that
$\langle b_yP_e \rangle$ (in unit of $\rm meV/cm^3$) increases from $0.24\pm
0.02$ at $z=0.14$ to $0.45\pm 0.02$ at $z=0.75$. These results lead to several
implications. (i) The hot gas fraction $f_{\rm gas}$ in clusters/groups
monotonically increase with halo mass, where $f_{\rm gas}$ of a $10^{14}
M_\odot/h$ halo is $\sim 50\%$ ($25\%$) of the cosmic mean at $z=0.14\ (0.75)$.
(ii) By comparing the 1h- and 2h-terms, we obtain tentative constraint on the
thermal energy of unbound gas. (iii) The above results lead to significant
suppression of matter and weak lensing power spectrum at small scales. These
implications are important for astrophysics and cosmology, and we will further
investigate them with improved data and gas modeling.
