Heat conduction theory stipulates that two thermo-physical properties of materials: the thermal conductivity “k” and the thermal diffusivity “α” influence the temperature evolution in regular and irregular bodies as a response to various cooling/heating conditions. The traditional statement involving the two thermo-physical properties is examined at length in the present study for the case of a semi-infinite region. The primary objective of the present study is to investigate the influence of the less known thermo-physical property called the thermal effusivity “e” on the incipient surface temperature rise in a semi-infinite body affected by uniform surface heat flux. The secondary objective of the study is to identify a key figure of merit named the dimensionless threshold time that separates the incipient temperature elevation in a semi-infinite region from the incipient temperature elevation in a large wall of finite thickness under the same uniform surface heat flux. The outcome of the methodical analysis suggests that the accurate estimate for the dimensionless threshold time τ_th in the semi-infinite region should be 0.10.