The evaluation of the tire tread viscoelastic characteristics, especially by means of non-destructive procedures, is a particularly interesting topic for motorsport teams and companies, used to work with unknown and confidential compounds. The availability of such information would define new scenarios in vehicle analysis field, as the possibility to provide physical inputs to tire grip models or the study of the suspensions setup able to make tires work inside their optimal thermal working range. The employment of commercial devices allows to select by means of specific indices the optimal combination of tires to be installed on a vehicle, but it does not provide any information physically correlated with the tread polymers characteristics. The aim of the presented activity is the modelling of one of the cited devices, a dynamic dial indicator, interacting with a viscoelastic half-space. The obtained results allow, analyzing the signals acquired by the device, to identify the tread equivalent stiffness and damping as a function of tire working temperature, providing the basic guidelines for the development of an innovative procedure for a full non-destructive viscoelastic characterization of the tire compounds. Index Terms-Material non-destructive characterization, temperature effect, tire tread compound behavior, TSD, viscoelastic characteristics.