When the human hand touches a garment that is at a different temperature than the skin, heat exchange occurs between the hand and the fabric, and the warm-cool feeling is the very first sensation. This transient transfer of energy depends on the contact interface between the skin and the fabric, and the contact interface depends on many morphological and structural parameters like fiber morphology or yarn and fabric structure. This paper describes a new experimental device for measuring heat absorption of textile materials in a transient state. The link between the transient thermal behavior and the tribological properties of fabrics is then made to show the influence of contact interface and therefore the influence of morphological and structural parameters on heat transfer. This investigation involves two cotton varieties (Pima of Morocco and Kaba S of Benin), two yarn structures (single and two-ply yarns), and three stitch lengths of jersey fabrics.