The techniques of thermal remote sensing (TIR) were applied in environmental studies especially for the extraction of the surface temperature. These techniques are the only available methods for the extraction of the surface temperature (Coll et al., 2005). Many authors have studied this parameter and proposed specific algorithms for its extraction from satellite imaging. Abdellaoui (1985) proposed a model for the relationship of the air temperature near the ground for the spatial extension of surface-based parameters models; Abdellaoui et al. (1986) proposed a global analysis model of energy balance at the soil-atmosphere interface that extracts the daily changes in surface temperature and evapotranspiration and an average value of thermal inertia; (Becker et Li, 1990) applied the split-window method on the earth's surface by taking into consideration the surface emissivity; (Sobrino et al., 1996) have developed a split-window algorithm for estimating the surface temperature by providing split-window coefficients adapted to ATSR sensor. (Gillespie et al., 1998) applied the TES method that uses a separation approach of the temperature and emissivity to find the surface temperature. (Qin et al., 2001a) have found it useful to focus on a single thermal band by developing a single-window algorithm for extracting the surface temperature from Landsat TM6 Data. Some conventional image processing software such as ENVI, IDRISSI, ERDAS incorporate a module for generating a surface temperature image using the calibration and adjustment parameters.
Thermal bands available in many remote sensing sensors are used to monitor the water temperature of rivers and streams for assessing changes in the riverine ecosystem. While direct in situ water temperature collection efforts provide point samples but are cost-prohibitive for characterizing stream temperatures across large spatial scales, especially for small, remote streams. In contrast, satellite thermal infrared imagery may provide a spatially extensive means of monitoring riverine water temperature.
Please refer to the following book chapter which covers comprehensively "Thermal Infrared remote sensing of Water Temperature in Riverine Landscapes".
Chapter Thermal Infrared Remote Sensing of Water Temperature in Rive...
You can use both MODIS Aqua and Terra, just make sure that coordinates coincide with river bed. Anyway, you can get the surface temperature only with some error on real data For the further investigations I suggest to use more accurate method of in-situ measurements using temperature loggers. The time resolution is high (up to few measurements per second), no any restrictions by depth or weather conditions.