The first Advanced Microwave Sounding Unit temperature sounder (AMSU-A) was launched on the NOAA-15 satellite on 13 May 1998. The AMSU-A’s higher spatial and radiometric resolutions provide more useful information on the strength of the middle- and upper-tropospheric warm cores associated with tropical cyclones than have previous microwave temperature sounders. The gradient wind relationship suggests that the temperature gradient near the core of tropical cyclones increases nonlinearly with wind speed. The gradient wind equation is recast to include AMSU-A-derived variables. Stepwise regression is used to determine which of these variables is most closely related to maximum sustained winds (Vmax). The satellite variables investigated include the radially averaged gradients at two spatial resolutions of AMSU-A channels 1–10 Tb data (δrTb), the squares of these gradients, a channel-15-based scattering index (SI89), and area-averaged Tb. Calculations of Tb and δrTb from mesoscale model simulations of Andrew (1992) reveal the effects of the AMSU spatial sampling on the cyclone warm core presentation. Stepwise regression of 66 AMSU-A terms against National Hurricane Center Vmax estimates from the 1998 and 1999 Atlantic hurricane season confirms the existence of a nonlinear relationship between wind speed and radially averaged temperature gradients near the cyclone warm core. Of six regression terms, four are dominated by temperature information, and two are interpreted as correcting for hydrometeor contamination. Jackknifed regressions were performed to estimate the algorithm performance on independent data. For the 82 cases that had in situ measurements of Vmax, the average error standard deviation was 4.7 m s−1. For 108 cases without in situ wind data, the average error standard deviation was 7.5 m s−1. Operational considerations, including the detection of weak cyclones and false alarm reduction, are also discussed.