Chirp-Pulse Microwave Computerized Tomography (CP-MCT) is a technique designed to image temperature variations inside the body. In the prototype developed at Niigata University images are obtained by means of the basic algorithm of tomography, namely the filtered backprojection. The purpose of this paper is to develop an improved linear model for data reduction. We introduce a methods, based on scattering theory, for computing the projections of a small phantom and we use these projections for defining the response function of the system. Our results also indicate that CP-MCT data are related to the variations of the attenuation constant inside the body. We conclude that, if these variations are sufficiently smooth, then CP-MCT projections can depend linearly on the distribution of the attenuation constant through the response function of the system.