This paper extends the algorithm of Evolutionary Structural Optimization to shape and topology design problems subjected to steady heat conduction. This extension incorporates an evolutionary iterative process into finite element heat solutions. During each iteration two basic steps are involved. Firstly, a finite element thermal solution is carried out for the current structure. Secondly, a small part of the material which cannot effectively contribute to the functionality of transferring heat is removed. Examples demonstrate the proposed evolutionary procedure being effective in solving heat conduction problems, which conventionally require sophisticated mathematical programming techniques.