Chirp-pulse microwave computed tomography (CP-MCT) is a technique for imaging the distribution of temperature variations inside biological tissues. Even if resolution and contrast are adequate to this purpose, a further improvement of image quality is desirable. In this paper, we discuss the blur of CP-MCT images and we propose a method for estimating the corresponding point spread function (PSF). To this purpose we use both a measured and a computed projection of a cylindrical phantom. We find a good agreement between the two cases. Finally the estimated PSF is used for deconvolving data corresponding to various kinds of cylindrical phantoms. We use an iterative nonlinear deconvolution method which assures nonnegative solutions and we demonstrate the improvement of image quality which can be obtained in such a way.