<p>This paper presents a shape optimisation (SO) method for the three-dimensional dissipative wave equation in the time domain. Building upon existing work on the standard wave equation, we derive a novel shape derivative using the adjoint variable method. This derivative, expressed solely in terms of boundary integrals, is then discretised within a NURBS-based framework for representing the surface of acoustic scatterers. The resulting sensitivities with respect to the NURBS control points are employed as the gradient of the objective functional in a quasi-Newton optimisation algorithm. Both the primary and adjoint wave equations are solved using the time-domain boundary element method recently developed by the first author, with enhancements to address instability issues encountered in homogeneous Dirichlet problems. The effectiveness of the proposed SO system is demonstrated through sensitivity analyses and two validation problems, comparing the results for dissipative and non-dissipative cases.</p>