  This work investigated the first-chance survival probabilities of highly
excited compound superheavy nuclei in the prospect of synthesizing new
superheavy elements. The main feature of our modelings is the adoption of
microscopic temperature dependent fission barriers in calculations of fission
rates. A simple derivation is demonstrated to elucidate the connection between
Bohr-Wheeler statistical model and imaginary free energy method, obtaining a
new formula for fission rates. The best modeling is chosen with respect to
reproducing the experimental fission probability of $^{210}$Po. Systematic
studies of fission and survival probabilities of No, Fl, Og, and $Z$=120
compound nuclei are performed. Results show large discrepancies by different
models for survival probabilities of superheavy nuclei although they are close
for $^{210}$Po. We see that the first-chance survival probabilities of $Z$=120
are comparable to that of Fl and Og.
