Recently, the effect of temperature on the mechanical property (the Young's modulus) of the single-layer molybdenum disulfide (SLMoS2) is shown to be insignificant, which is obviously incompatible with the previously published result, i. e. the Young's modulus of SLMOS2 decreases monotonically as temperature increases. Aiming at clarifying the relationships between the mechanical properties of the single-layer molybdenum disulfide (SLMoS2) along the armchair (AC) and zigzag (ZZ) directions and the temperature, classical molecular dynamics (MD) simulations are performed to stretch the SLMoS2 along the AC and ZZ directions at the temperatures ranging from 1 K to 800 K by using the Stillinger-Weber (SW) interatomic potentials in this paper. The mechanical properties of SLMoS2 at the temperatures ranging from 1 K to 800 K, including ultimate strength, ultimate strain, and Young's Modulus, are calculated based on the stress-strain results obtained from the simulations. Results are obtained and given as follows. (1) The mechanical properties of the SLMoS2, including the ultimate strength and Young's modulus, are found to monotonically decrease as temperature increases. Increasing the temperature, the ultimate strength of SLMoS2 in the AC direction drops faster than in the ZZ direction, whereas the Young's modulus of SLMoS2 in the ZZ direction decreases quicker than in the AC direction, which means that the chirality effect on the ultimate strength is remarkably different from the Young's modulus of SLMoS2. However, the ultimate strain in the ZZ direction at the temperatures in a range from 1 K to 800 K is close to that in the AC direction, which means that the effect of chirality on the ultimate strain is insignificant. (2) Unlike the published results in the literature, the phase transition of SLMoS2 is found to only occur at a temperature of 1 K and at the moment of initial crack formation as tensiled along the ZZ direction, and the new phase of quadrilateral structure keeps stable after unloading. (3) The linear thermal expansion coefficients along the ZZ and AC directions are also measured, the magnitudes of which are found to be consistent with the published experimental results. Our simulation results support the viewpoint that the effect of the temperature on the mechanical property of SLMoS2 is significant, and the SLMoS2 can be regarded as an anisotropic material as the chirality effect cannot be ignored. The linear thermal expansion coefficients obtained with MD simulation are all in good agreement with the experimental data.