Thermodiffusive transport of trace elements that play important roles in living organisms, such as molybdenum, nickel, copper, and vanadium, was studied in a nonisothermal biphasic system comprised of a liquid solution and jelly layers. Our intent was to mimic the effects of temperature gradients on prebiological evolution. Conditions were found, similar to those probably existing during development of early eobionts, under which all the elements tested were concentrated within the heated jelly. Nonisothermal matter transport through grossly porous artificial membranes--the process of thermodialysis--was next investigated to assess the behavior of compartmentalized, i.e., membrane bound, eobionts. Particular interest was dedicated to the continuity of nonisothermal transport phenomena in the homogeneous and heterogeneous (membrane) systems and to the ability of compartmentalized eobionts to withstand osmotic swelling by means of thermoosmotic transport. Interestingly enough, under the experimental conditions adopted, sodium/potassium countertransport is also found, suggesting a very early physicochemical origin of the sodium-potassium pump. Surprisingly enough, evidence of teleonomic behavior appears in those very simple analogs of prebiological systems.