A long-term static position causes inter alia hypoxia, poor blood circulation, slowing down of the metabolism, and problems in air and heat transport, which in consequence lead to the occurrence of bedsores. In the design of seats and mattresses for people with impaired mobility, advanced textile and composite materials should be used to improve safety and comfort. This functionality can be obtained using spatial textile materials. The aim of the research was to assess the impact of two unmodified woven relief structures I.0 and II.0 made of different yarns and ones modified by inserting linear elements (1: braided round tape and 2: polyethylene tube) to their rib tunnel on the heat transport and on the pressure distribution under loading of 0.5, 1, and 2 N. Element 1 lowers the value of average pressure on the fabrics I.1 and II.1, respectively, by 6.9% and 3.5% at the lowest loading and by 9.8% and 4.6% at the highest loading. For fabric II.2 with element 2, the decrease is of 10.4% and 8.4%, respectively. The thermal conductivity values increase by 8.8%, 9.4%, and 40.1%, respectively for I.1, II.1, and II.2. The pressure distribution and thermal characteristic of the fabrics depend on the type of yarn, the structure of ribs, and the linear element and its fit to the rib tunnel.