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In this paper, the electrical transport, thermal transport, and thermoelectric properties of three new Janus STe$_{2}$, SeTe$_{2}$, and Se$_{2}$Te monolayers are systematically studied by first-principles calculations, as well as the comparative with available literature's results using different methods. It is found that the Seebeck coefficient and conductivity have opposite dependence on temperature, and we illustrate this phenomenon in detail. The decrease of the thermoelectric power factor (PF) with temperature originates from the decrease in conductivity. To obtain accurate and convergent lattice thermal conductivity, the root mean square (RMS) is calculated to obtain a reasonable cutoff radius for the calculation of third-order forces. Janus STe$_{2}$, SeTe$_{2}$, and Se$_{2}$Te monolayers exhibit ultra-low lattice thermal conductivity of 0.2, 0.133, and 4.81$\times10^{-4}$ W/mK at 300 K, which result from the strong coupling effect between the acoustic mode and the low-frequency optical branch, low phonon group velocity, small phonon lifetime, and large anharmonicity. Consequently, ultra-high $\textit{ZT}$ values of 2.11 (2.09), 3.28 (4.24), and 3.40 (6.51) for n-type(p-type) carrier doping of STe$_{2}$, SeTe$_{2}$, and Se$_{2}$Te are obtained, indicating that they are promising thermoelectric materials.