  The holographic complexity of a `black' non-susy $D3$-brane is computed. The
difference in the holographic complexity between this geometry in the
Fefferman-Graham coordinates and that of the $AdS_5$ geometry is obtained for a
strip type subsystem. This is then related to the changes in the energy and the
entanglement entropy of the system. We next take the high temperature limit of
the change in complexity and observe that it scales with the temperature in the
same way as the holographic entanglement entropy. The crossover of the
holographic complexity to its corresponding thermal counterpart is similar to
the corresponding crossover of the holographic entanglement entropy in the high
temperature limit. We further repeat the analysis for $\mathcal{N} =4$ super
Yang-Mills theory and observe a similar behaviour.
