In this paper, a new control scheme for high temperature trajectory following problems is presented. The problem of reproducing on proper test articles the thermal stress conditions occurring on parts of space vehicles during the reentry into atmosphere is considered. The model of the thermal process, in the lumped parameter domain, is described by a quasi-linear system depending on a number of parameters that are uncertain and varying with the operating conditions. An ad hoc trajectory following control system is proposed together with a robust performance analysis which makes use of the concept of quadratic stability with an H-infinity norm bound. The analysis technique allows to evaluate the stability of the closed loop system in the presence of time varying parameters and uncertainties, and the rejection of disturbances acting at the system input. An LMI based observer synthesis procedure is proposed to increase the closed loop system performance.