Resting state functional magnetic resonance imaging (rsfMRI) data provides a unique window for the investigation of the human brain's intrinsic functional mechanism. However, it is still an open question how to analyze and model functional brain connectivity networks via rsfMRI data due to the variability of different individual brains, noisy signals from rsfMRI data, and technical limitations of current rsfMRI data decomposition methods. In this work, we proposed a two-stage deep learning framework for both temporal and spatial analysis of functional brain networks with an application on autism spectrum disorder (ASD) rsfMRI data. This framework tackled the abovementioned challenges in these aspects: reducing noises in rsfMRI raw data, establishing functional network correspondence across various individual brains, and composing multiple functional networks into a compact representation. In general, our proposed framework offers a novel scheme for comprehensive and systematic spatial-temporal resting state network modeling. Our experimental results on the ABIDE ASD dataset showed promising results in discovering discriminative functional networks compared with traditional analysis. Furthermore, our work provided a new insight into ASD that ASD's functional activity abnormalities tend to be more composite and systematic, other than being localized.