For LST retrieval, long-wave infra-red satellite observations are commonly used. Either single-band data along with a radiative transfer model, or a split-window technique (two adjacent TIR bands) to allow for atmospheric corrections (see Wan and Dozier, 1996). Such data are available from many sensors; the choice of sensor depends on the requirements of your study. You can find a lot of documentation and data in the webpage of EUMETSAT's Satellite Facility on Land Surface Analysis (http://landsaf.meteo.pt/)
You can retrieval LST from thermal bands of Landsat, ASTER, SEVIRI, AVHRR and Sentinel 3. There are different methods for estimate LST such as: Single-channel Algorithms, Split-Window algorithms and Multichannel Algorithms. The result be more accurate with doing Atmospheric and Emissivity correction.
For Landsat 8, you can look at this open access article:
If it is a satellite with two thermal bands (like Landsat 8 or MODIS), the Split-Window (SW) algorithm is the best choice (easy and efficient). I myself used SW in three of my papers and found it accurate and easy to apply. Also, I used the online atmospheric correction tool provided by NASA (http://atmcorr.gsfc.nasa.gov/). This is also good but you can't apply it for entire image and it is point base. Also, I attached a file that are some parts of my own paper on LST estimation using Landsat 8 data. Hope it helps you.