Thermal conductivity is one of the most important physical properties of rocks. However, not only is direct measurement of thermal conductivity time-consuming and labor-intensive, direct measurement of unexposed geological units is not possible. One solution to this problem is to link thermal conductivity with wave velocity, which can be measured onsite. Here, thermal conductivity tests were conducted on samples recovered from wave velocity experiments. Through the comprehensive analysis of thermal conductivity, chemical composition, mineral composition, and ultrasonic velocity, it was preliminarily found that the thermal conductivity of rocks is a piecewise function of wave velocity. In two subdomains (i.e., rocks with low or no quartz content, and rocks with a higher quartz content), the thermal conductivity and wave velocity are approximately linearly related. Confirmation of this law by a large amount of experimental data would provide great convenience for obtaining the in-situ thermal conductivity of deep earth and a better understanding of the thermal structure of the lithosphere.