The alpha decay half-lives for $^{171-189}\mathrm{Hg}$ isotopes have been computed using the Gamow-like model (GLM), modified Gamow-like model (MGLM1), temperature-independent Coulomb and proximity potential model (CPPM), and temperature-dependent Coulomb and proximity potential model (CPPMT). New variable parameter sets were numerically calculated for the $^{171-189}\mathrm{Hg}$ using the modified Gamow-like model (termed MGLM2). The results of the computed standard deviation indicates that the modified Gamow-like model (MGLM2) and the temperature-dependent Coulomb and proximity potential model give the least deviation from available experimental values, and therefore suggests that the two models (MGLM2 and CPPMT) are the most suitable for the evaluation of $\alpha$-decay half-lives for the $\mathrm{Hg}$ isotopes.