The differential equations which describe the one-dimensional temperature distribution in a convectively cooled thermoelement with variable cross-sectional area are presented and solved analytically with appropriate boundary conditions. Expressions for the maximum heat pumping and the maximum temperature difference are developed. Sample computations for two families of shapes are presented, and a comparison is made between the performance of a constant-area element and the performance of a variable-area element. It is shown that under certain conditions shaping the element can enhance the performance gains to be derived from the use of convective cooling along the length of the element. The results seem to indicate that in certain special applications—especially those in which it would be desirable to use little or no insulation along the element near the cold junction—shaped, cooled elements will offer some performance advantages over cooled, constant-area elements.