A fully non-linear analysis of forcings' influences on temperatures is performed in the climate system by means of neural network modeling. In doing so, we adopt a feed-forward neural network model with a peculiar backpropagation training. Two case studies are investigated, in order to establish the main factors that drove the temperature behavior at both global and regional scales in the last 140 years. In particular, our neural network model shows the ability to catch nonlinear relationships among these variables and to reconstruct temperature records with a high degree of accuracy. In this framework, we clearly show the need of including anthropogenic inputs for explaining the temperature behavior at global scale and recognize the role of El Niņo Southern Oscillation for catching the interannual variability of temperature data. An interesting analysis of the residuals shows that the variance not explained by our model is probably due almost completely to the natural variability of climate system. Furthermore, we analyse the relative influence of global forcings and a regional circulation pattern in determining the winter temperatures in Central England, showing that the North Atlantic Oscillation represents the driven element in this case study. Our modelling activity and results can be very useful for simple assessments of relationships in the complex climate system and for identifying the fundamental elements leading to a successful downscaling of Atmosphere-Ocean General Circulation Models.