It has been a key topic to decompose the brain's spatial/temporal function networks from 4D functional magnetic resonance imaging (fMRI) data. With the advantages of robust and meaningful brain pattern extraction, deep neural networks have been shown to be more powerful and flexible in fMRI data modeling than other traditional methods. However, the challenge of designing neural network architecture for high-dimensional and complex fMRI data has also been realized recently. In this paper, we propose a new spatial/temporal differentiable neural architecture search algorithm (ST-DARTS) for optimal brain network decomposition. The core idea of ST-DARTS is to optimize the inner cell structure of the vanilla recurrent neural network (RNN) in order to effectively decompose spatial/temporal brain function networks from fMRI data. Based on the evaluations on all seven fMRI tasks in human connectome project (HCP) dataset, the ST-DARTS model is shown to perform promisingly, both spatially (i.e., it can recognize the most stimuli-correlated spatial brain network activation that is very similar to the benchmark) and temporally (i.e., its temporal activity is highly positively correlated with the task-design). To further improve the efficiency of ST-DARTS model, we introduce a flexible early-stopping mechanism, named as ST-DARTS+, which further improves experimental results significantly. To our best knowledge, the proposed ST-DARTS and ST-DARTS+ models are among the early efforts in optimally decomposing spatial/temporal brain function networks from fMRI data with neural architecture search strategy and they demonstrate great promise.