Can you use Landsat 7 to make studies of land surface temperature, even though it has the scan line problem?

Landsat has a unique combination of spatial resolution and revisiting for thermal band, so you don't have much other choice during the scan line issue period.

With the other Landsat bands, you can fill the gaps by combining successive looks of the satellite, but I would not do it with thermal bands because t could change a lot. Spatial interpolation could be used to fill the gaps, but LST could change abruptly if the land cover changes (e.g. above a water body), therefore it is a bit dangerous as it gives a false impression of increased spatial information. I would only apply interpolation if my land cover is homogeneous. Otherwise, a proper handling of missing data could be better than the guessing.

At coarser resolution, you could use MODIS. I would consider it as a good alternative to the missing data of Landsat. If if you try the interpolation, you could test the robustness of your method by comparing downsampled values with MODIS.