Saleem, you may use the LANDSAT series, i.e. LANDSAT 8, 7(ETM+) and 5 (TM) depending upon the time period you are interested. All of them have a spatial resolution of 30 metres. Besides MODIS also have LST (land surface temperature) products, daily data as well as 8day data (both having spatial resolution of 1 Km).
The world is a big place, and water appears in many different places. Tundra ponds? Mid-ocean? Canopy obscure tropical streams? It is helpful if you specify your area of interest ( like give the extents, max/min, lat/long for instance ) and any other conditions which pertain.
You need to first determine which sensor/mission you are going to use for this purpose? Are you using Landsat 8, 7, or 5? You need to use thier thermal bands and calculate the brightness value (BV) and land surface emissivity (LSE) to get to the LST. MODIS also produces LST as product, however, its spatial resolution is relatively coarse (1km). So another thing to consider is your geographical area extent and its scale.
If it's a time series, then you'll need to specify the years as regards the Landsat images that you'll download. If you know programming, GEE offers a better interface of assessing such dataset.
Saleem - you can try https://earthdata.nasa.gov/search?q=MODIS+LST to get Land Surface Temperature datasets from NASA Land Processes Distributed Active Archive Center (LP DAAC).
If you use Landsat data then you can get land surface temperature by calculating the BV and LSE of the thermal bands of the Landsat data (i.e. if landsat-7 then band 6). Landsat data are also free accessible.
Identification of wetland and water bodies is very interesting topic in remote sensing. Mostly people are using satellite indices with LULC. These are very old methods. you can use CNN or deep learning .
You can classify land cover classes and estimate land surface temperature and perform a combined tool in Arc GIS between LST and LULC. This will give you temperature variations in different LULC as well as waterbodies/wetlands
You could follow our paper for the calculating water surface temperature by following these steps: "Glacial Lake Dynamics and Lake Surface Temperature Assessment along the Kangchengayo-Pauhunri Massif, Sikkim Himalaya, 1988–2014". Remote Sensing Applications Society and Environment 9(6)
To measure sea surface temperature (SST), scientists deploy temperature sensors on satellites, buoys, ships, ocean reference stations, and through marine telemetry. The NOAA-led U.S. Integrated Ocean Observing System (IOOS®) and NOAA's Center for Satellite Applications and Research (STAR) merge their data to provide SSTs worldwide https://oceanservice.noaa.gov/facts/sea-surface-temperature.html