Global-scale Observations of Limb and Disk (GOLD) disk measurements of far ultraviolet molecular nitrogen band emissions are used to retrieve column integrated disk temperatures (T$_{disk}$), which are representative of the lower-and-middle thermosphere. The present work develops a new approach to assimilate the T$_{disk}$ in the Whole Atmosphere Community Climate Model with thermosphere-ionosphere eXtension (WACCMX) using the Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter. A total of 9 days of data during 1 to 9 November 2018 are assimilated. Analysis state variables such as thermospheric effective temperature (T$_{eff}$), ratio of atomic oxygen to molecular nitrogen column densities (O/N$_2$), and column electron content are compared with a control simulation that is only constrained up to $\sim$50 km. It is observed that assimilation of the GOLD T$_{disk}$ improves the analysis states when compared with the control simulation. The analysis states, particularly, T$_{eff}$, O/N$_2$, and column electron contents are also compared with their measurement counterparts for the validation of the assimilation. T$_{eff}$ and O/N$_2$ are compared with GOLD T$_{disk}$ and O/N$_2$. While, the Electron Column Density (ECD) from the analyses is compared with ground based Total Electron Content (TEC) measurements from Global Navigational Satellite System (GNSS) receivers. Root Mean Square Error (RMSE) improvements in T$_{eff}$ and O/N$_2$ are about 12.8% and 13.2%, respectively. The RMSE improvement in analyses ECD is about 8% compared to control simulation.