Estimating the sensible heat flux H over sparse vegetation from thermal infrared temperature requires an estimate of the excess resistance r(r) to the aerodynamic resistance. This excess resistance has been commonly expressed as a function of the dimensionless parameter kB(-1). Experimental analysis of this parameter over diverse sparse vegetation in semi-arid areas showed a large and unexpected range of variation. The flux and ground-based thermal infrared data of the East Central Site of HAPEX-Sahel were used in this paper to study the behaviour of the kB(-1) parameter and to compare these results with the conclusions of previous studies. At first, the global accuracy of the; estimation of H as a function of the kB(-1) value was analysed; it was found that overestimating kB has less serious consequences than underestimating it. Then, optimal values of kB(-1), obtained for each site (one fallow savannah site and two millet sites), ranged from 5.1 to 10.2, with significantly different values for the two millet sites. The corresponding Root Mean Square Error (RMSE) between estimated and measured H ranged from 43 to 67 W m(-2). Finally, the instantaneous Values of kB(-1) proved to be highly variable and the parameterization of kB(-1) proposed by Kustas et al. (1989) as a function of u(T-r - T-a) appeared valid only for high H values. For lower values, the slope of this relationship must be adjusted for each class of H. All the previous results confirmed that a constant value can neither be assumed for semi-arid areas nor for a given type of vegetation and that further studies are needed to understand its behaviour. Considering the difficulty in predicting the kB(-1) values, a different approach based on the relationship observed between aerodynamic and radiometric temperatures was investigated. This approach gave more accurate estimate of H (RMSE between 35 and 48 W m(-2)), but remains at this stage purely empirical. Further investigation is now needed to predict the parameterization of this approach.