I am working on a trend analysis of at-satellite temperatures (brightness temperature) using Landsat 5, 7 and 8 thermal bands. For the visual and infrared bands I used the sensor harmonization function proposed by Roy et al.Article Characterization of Landsat-7 to Landsat-8 reflective wavele...
However, for the thermal bands no transformation coefficients were calculated. Is there the necessity to transform the thermal bands?
From what I understand, yes, the infrared bands should still be harmonized. I had the same question and was unable to find any citations for how to do this. The most recent publication I found that mentions thermal harmonization says that this harmonization is "complicated" and leaves it at that. Harmonizing surface reflectance between Landsat-7 ETM + , Landsat-8 OLI, and Sentinel-2 MSI over China | SpringerLink
However, collection 2 level 2 data should have relatively minor errors when comparing between satellites. If the higest accuracy Landsat thermal data is required for something like a timeseries analysis, the best option is to use the ARD product provided by USGS. This dataset is (currently) only available for the United States with plans for a global release at an unspecified point in the future.