A consistent determination of the temperature of the intergalactic medium at redshift < z >=2.4

We present new measurements of the thermal state of the intergalactic medium (IGM) at z similar to 2.4 derived from absorption line profiles in the Ly alpha forest. We use a large set of high-resolution hydrodynamical simulations to calibrate the relationship between the temperature-density (T-delta) relation in the IGM and the distribution of H i column densities, N-H I, and velocity widths, N-H I, of discrete Ly alpha forest absorbers. This calibration is then applied to the measurement of the lower cut-off of the N-H I-N-H I distribution recently presented by Rudie et al. We infer a power-law T-delta relation, T = T-0 delta(gamma - 1), with a temperature at mean density, T-0 = [1.00(-0.21)(+0.32)] x 10(4) k and slope (gamma - 1) = 0.54 +/- 0.11. The slope is fully consistent with that advocated by the analysis of Rudie et al.; however, the temperature at mean density is lower by almost a factor of 2, primarily due to an adjustment in the relationship between column density and physical density assumed by these authors. These new results are in excellent agreement with the recent temperature measurements of Becker et al., based on the curvature of the transmitted flux in the Ly alpha forest. This suggests that the thermal state of the IGM at this redshift is reasonably well characterized over the range of densities probed by these methods.