This is the first in a series of two papers on the thermal inertia estimation from satellite data. In this paper we have evaluated the behavior of three algorithms to retrieve surface thermal inertia from NOAA-advanced very high resolution radiometer (AVHRR) data. These are Price's <1977> algorithm, and two different algorithms based on the model of Xue and Cracknell <1995>; Xue and Cracknell's algorithm (XC), and a new approach which we have named FTA (four temperatures algorithm) since it uses four AVHRR measurements (XC plus two from NOAA morning satellites). The main advantage of the FTA is that it only uses satellite data. The algorithms were tested with a set of in situ measurements taken over a region of Niger in the frame of the Hydrologic Atmospheric Pilot Experiment-Sahel. The analysis was done in two different ways: (1) by comparing the ST (surface temperature) predicted by the algorithms with the measured ones every 10 minutes, and (2) by comparing the predicted and measured maximum and minimum ST values as well as their respective times. Our results indicate that the FTA is the most appropriate algorithm for presenting the diurnal cycle of the ground ST with these experimental data. For 90% of the cases the absolute difference between predicted and measured STs is lower than 2 K, with a standard deviation of 1.5 K that improves to 1 K when predicting the maximum and minimum STs. The FTA also predicts their respective times with a standard deviation of less than 30 min. These results suggest that it is possible to predict the minimum ST and corresponding time from NOAA data, which might be useful to forecast frost during nights of radiative cooling (cloudless and calm wind). ¿ 1999 American Geophysical Union