This paper studies the thermal response on the mold surface of a circular cavity in the preheating process by high-temperature gas via a numerical approach, where the heat and mass transfer inside the cavity and mold are predicted by a two-fluid model. The dimensionless parameter group is identified,from a dimensional analysis of the gas preheating problem. The correlations among dimensionless parameters are established by a least square method applied to the numerical predictions. The upper limit of the temperature rise on the cavity surface at a given gas flow rate is found approximately proportional to the square root of Q* and h*, respectively. The lower limit of gas flow rate to achieve a given temperature rise on the cavity surface is inversely proportional to h* but grows with (Q*)(1.5). The first limiting line to describe the dependence of Q* on t* is independent of h* and T*, but the second one is governed by Q*(c). For reaching a specified temperature rise on the cavity surface, the growth in the thickness of thermal resistive layer reduces the required preheating time but increases the corresponding gas flow rate. The dependence of (t*(f), Q*(f)) on the parameter group (T*, h*) is given in this study to obtain the reasonable combinations of (t*(f,) Q*(f)) based on the balance between the allowable preheating time and heating capacity.