Within the framework of the present work, studies are being carried out to select the tooling material for the automated placement of the thermoplastic prepreg. A mathematical model of the heating of the tooling and a thermoplastic prepreg tape with an automated placement of the prepreg on the mandrel is developed. In the framework of numerical experiments, two rigs made of steel and carbon fiber were considered. Based on the results of numerical experiments, the temperature field distributions in the laid out part and in the tooling were obtained. The analysis of the obtained results revealed that when using metal tools, a considerable heat removal from the heated layers of the thermoplastic is observed, which can significantly influence the crystallization process of the thermoplastic. Also on the carbon-fiber tooling, the laser warming spot is more localized than in the metallic one. On the basis of the data obtained, the linear deformation of the rigging was calculated, it was found that the maximum deformations in the steel tooling are three times higher than the maximum deformations in the carbon fiber. It is determined that when using metal equipment, a significant heat removal from the heated layers of the thermoplastic is observed.