It has been noticed that the Landsat 8 Thermal Infrared Sensor (TIRS) had an issue with stray light since its launch in 2013. This artifact is due to out-of-field radiance that scatters onto the TIRS focal plane. Much effort has been taken to develop an algorithm to remove this artifact. One proposed approach involves using TIRS data itself (referred to as TIRS-on-TIRS) to retrieve the true sensor-reaching radiance. This approach has been proven to be operational and supports the TIRS Collection-1 product. A methodology of calibrating the TIRS sensor with information from the Geostationary Operational Environmental Satellite (GOES) instrument may optimally reduce the stray light effect for special cases where there is a large temperature contrast between the edge of the TIRS image and out-of-field radiance (referred to as GOES-on-TIRS). This paper illustrates a GOES to TIRS conversion (GTTC) algorithm with the North American Regional Reanalysis (NARR) data to support the GOES-on-TIRS method. Results show this GOES_TIRS correction method performs similarly to the TIRS Collection-1 product. Additionally, a simplified methodology is proposed to improve the GOES data processing which can operationalize the GOES-on-TIRS algorithm. Results also show that, using the proposed algorithm with these special cases, the maximum difference between the Collection-1 product and the GOES-on-TIRS correction results in a temperature difference from 0.5% to 0.7%.