We report a method for real-time three-dimensional monitoring of thermal therapy through the use of noncontact microwave imaging. This method is predicated on using microwaves to image changes in the dielectric properties of tissue with changing temperature. Instead of the precomputed linear Born approximation that was used in prior work to speed up the frame-to-frame inversions, here we use the nonlinear distorted Born iterative method (DBIM) to solve the electric volume integral equation (VIE) to image the temperature change. This is made possible by using a recently developed graphic processing unit accelerated conformal finite difference time domain method to solve the forward problem and update the electric field in the monitored region in each DBIM iteration. Compared to our previous work, this approach provides a far superior approximation of the electric field within the VIE, and thus yields a more accurate reconstruction of tissue temperature change. The proposed method is validated using a realistic numerical model of interstitial thermal therapy for a deep-seated brain lesion. With the new DBIM, we reduced the average estimation error of the mean temperature within the region of interest from 2.5 to 1.0 for the noise-free case, and from 2.9 to 1.7 for the 2% background noise case.