I'm looking for SST data for the Mediterranean Sea, especially for the eastern part of it. Specifically, I seeking a database from which I can be able to collect surface temperature for each decade or year.
You can access and review without any cost the data that the NOAA has for SST. Its really easy and they have charts that will allow you to analyze the information for each day or month, and their data are reliable. Here's the link so you can check it out.
Yes I used NOAA to obtain SST for Ghana without an issue. This publication may also be useful to you. Freeman E, et al. 2017. IOCADS Release 3.0: a major update to the historical marine climate 361 record. International Journal of Climatology 37:2211-2232.
The longest available (since 1982) high resolution, L4 satellite-derived dataset is the one from the Copernicus Marine Environment Monitoring Service (CMEMS, http://marine.copernicus.eu). The very high spatial (~4x4 km) and daily temporal resolution has been shown to be suitable for studying SST trends and anomalies even at regional scales. It is distributed freely under the name SST_MED_SST_L4_REP_OBSERVATIONS_010_021 in the CMEMS catalogue.
Sea Surface Temperature is measured in many ways and for different temperature. From your description it seems that you want to make a climatic (long term) assessment. for that I would use a reanalysis product. You can find many of those in reanalysis.org, but I think that for the Mediterranean I would recomend the copernicus (EEU) reanalysis https://resources.marine.copernicus.eu/?option=com_csw&view=details&product_id=MEDSEA_REANALYSIS_PHYS_006_004. These are netcdf files that requires some getting used to to work with but this work is eesential for any oceanographic work.