The atmospheric weighted mean temperature (Tm) is a key parameter in determining the precipitable water vapor (PWV). Many conventional meteorological parameter empirical models have a lower spatial resolution and poor regional applicability, resulting in lower accuracy in obtaining the Tm value in GNSS PWV retrieval. This paper will address an LSTM-ERATM model and evaluate the accuracy of calculating the atmospheric weighted temperature. Considering Tm's annual, semi-annual, and daily cycle characteristics, an ERATM model was developed based on the ERA5 data from 2017 to 2020 provided by the European Center for Mesoscale Weather Forecasts. Then the long short-term memory (LSTM) model was used to train the difference between the Tm values obtained by discrete integration of the ERA5 data and Tm values calculated by the ERATM model to enhance the accuracy of the ERATM model. We use the ERA5 and sounding data from 2021 to 2022 to compare and analyze the calculation effect of the LSTM-ERATM, ERATM, GPT3, NUB3, and Bevis models. The results show that the ERATM model has broad regional applicability and can provide high-accuracy atmospheric weighted mean temperature. Compared with the UNB3, GPT3, and Bevis models, the mean RMS value of the ERATM model is reduced by 43.4%, 3.4%, and 11.7% respectively when using the ERA5 data as the reference value, and reduced by 22.9%, 13.9%, and 0.2% respectively when using the sounding data as the reference value. Moreover, the accuracy of the LSTM-ERATM is generally better than ERATM at different time points and regions, which shows that the LSTM model effectively improves the accuracy of the ERATM model in calculating Tm. For example, the mean RMS values of LSTM-ERATM were reduced by 50.8%, 37.4%, 26.2%, and 18.9% in the next time points of 6:00, 12:00, 18:00, and 24:00 respectively when using the ERA5 data as the reference value, and reduced by 31.3%, 27.2%, 35.9%, and 8.6% respectively when using the sounding data as the reference value. The LSTM-ERATM model in this study provides a powerful tool to improve the accuracy of calculating Tm, which can provide more reliable data for meteorology and climate research.