Motivated by recent experimental observations on ultrathin Fe/Cu(001) films, we performed a theoretical analysis of magnetic domain pattern evolution in 2D Dipolar Frustrated Ising Ferromagnet. Due to the competition between long-ranged dipolar interaction and nearest neighbor ferromagnetic exchange interaction, the ground state is given by a succession of saturated domains of positive and negative magnetization, which alternate in a sharp striped pattern of characteristic domain width $h_{gs}$. Close to the Curie temperature $T_C$, the Mean Field theory predicts the occurrence of a cosine modulation with a much smaller spatial period $h(T_C)$. We recover these two limits in the whole temperature range $0\le T \le T_C$, where a magnetically ordered phase exists; the two regimes are connected continuously but, as translational invariance does not hold, the interplay between thermal fluctuations and the two competing interactions gives rise to a non-trivial magnetization profile at intermediate temperatures.