Learning suitable and well-performing dialogue behaviour in statistical spoken dialogue systems has been in the focus of research for many years. While most work which is based on reinforcement learning employs an objective measure like task success for modelling the reward signal, we use a reward based on user satisfaction estimation. We propose a novel estimator and show that it outperforms all previous estimators while learning temporal dependencies implicitly. Furthermore, we apply this novel user satisfaction estimation model live in simulated experiments where the satisfaction estimation model is trained on one domain and applied in many other domains which cover a similar task. We show that applying this model results in higher estimated satisfaction, similar task success rates and a higher robustness to noise.