A thermomolecular pressure associated with a thermal gradient produces the phenomenon known as frost heave' in moisture-containing frozen ground. Thermomolecular pressures can occur in any material. As described here it is known that frost heave or thermomolecular pressures can be exhibited by any material undergoing premelting,' where liquid exists at temperatures below the normal solid-liquid phase boundary. Yet, the recent work on [sup 4]He [Hiroi, et a., Phys. Rev.B 40, 6581 (1989)] is the first published study of thermomolecular pressure in nonaqueous material. The striking prominence of the effect presents advantages of further applications of thermomolecular pressure for fundamental research. This paper describes the phenomenon, outlines the theory and discusses some possible static and dynamic studies of quantum liquids.