Here, we show how the cooling performance of a volumetrically heated solid can be increased by embedding high-conductivity tree-shaped designs in it. The volume fraction occupied by the high-conductivity material is fixed. Embedding the high-conductivity material as trees in the solid decreases the maximum temperature more than three times compared with distributing the high-conductivity material uniformly throughout the solid. The maximum temperature decreases as the number of the bifurcation levels and the volume fraction of the highly conductive material increase. The thermal resistance of the cube is the lowest when the diameter ratio of the mother and daughter branches at each pairing junction is 2. Changing from T-shaped to Y-shaped designs and from two-dimensional to three-dimensional designs decrease the maximum and the volume averaged temperatures. The peak temperature is the lowest in three-dimensional and Y-shaped designs. This paper shows that the peak temperature of the heated solid can be decreased by only varying the shape of the high-conductivity tree embedded in it. Copyright (c) 2014 John Wiley & Sons, Ltd.