A two-phase isotropic optimal design problem within the context of the transient heat equation is considered. The objective is to minimize the average of the dissipated thermal energy during a time interval \([0,T]\). The authors study the asymptotic behavior, as \(T\) goes to infinity, of the solutions of the relaxed problem and prove that they converge to an optimal relaxed design of the corresponding two-phase optimization problem for the stationary heat equation. In particular, the authors study a necessary optimality condition for the parabolic problem and prove that optimal microstructures for this problem can be found among laminates of rank at most \(N\), the spatial dimension. Significant attention is paid to asymptotic analysis, when \(T\to \infty\), of that necessary optimality condition. At the end, results of numerical experiments are given.