This paper presents the results of experimental investigations into the influence of geometric parameters of a model material on the kinetics of thermo-mechanical processes under physical modelling conditions. Commercial PRIMO plasticine was used as the model material; due to its rheological stability and strong temperature dependence of mechanical properties, it is a suitable analogue material widely applied in physical modelling of metal forming processes. The main objective of the study was a quantitative evaluation of the cooling dynamics of cylindrical specimens with varying dimensions (D/H = 1, 10-50 mm) and the determination of the effect of volume variation on the average flow stress values. Static upsetting tests were conducted using an Instron 3369 universal testing machine under a constant deformation rate and reduced friction conditions. The results revealed a strong, nonlinear correlation between specimen volume and the time required to achieve complete temperature homogenisation. It was observed that during the initial cooling stage a rapid increase in flow stress occurred as a result of intensive heat dissipation. With increasing cooling time, the rate of change gradually decreased, asymptotically approaching a steady state in which the mechanical properties stabilised regardless of specimen size. A key outcome of this study is the formulation of a predictive mathematical model in the form of a second-order polynomial function describing the relationship between the optimal cooling time and specimen diameter. The high coefficient of determination confirms the reliability of the model for laboratory test optimisation. Empirical data showed that for specimens with a diameter of 50 mm, the time required for temperature stabilisation exceeded 35 hours, highlighting the importance of scale effects in the interpretation of physical modelling results. The developed approach enables the elimination of errors resulting from thermal non-uniformity of the model material, directly improving the accuracy of physical simulations of forging, rolling, and extrusion processes.