  Inspired by the recent discovery of a new polar metal LiReO$_3$ by K.
Murayama, \textit{et al}, we calculate the temperature($T$)-dependent crystal
structures of Li$B$O3 with $B$ = Ta, W, Re, Os, using the self-consistent
phonon (SCPH) theory. We have reproduced the experimentally observed
polar-nonpolar structural phase transitions and the transition temperatures
($T_c$) of LiTaO$_3$, LiReO$_3$, and LiOsO$_3$. From the calculation, we
predict that LiWO$_3$ is a polar metal, which is yet to be tested
experimentally. Upon doping electrons to the insulating LiTaO$_3$, the
predicted $T_c$ is quickly suppressed and approaches those of the polar metals.
Thus, there is a continuous crossover between ferroelectric insulators and
polar metals if we dope electrons to the polar metals. Investigating the
detailed material dependence of the interatomic force constants (IFCs), we
explicitly show that the suppression of $T_c$ in polar metals can be ascribed
to the screening of the long-range Li-O interaction, which is caused by the
presence of the itinerant electrons.
