Recently, the Internet of Things (IoT) receives significant interest due to its rapid development. But IoT applications still face two challenges: heterogeneity and large scale of IoT data. Therefore, how to efficiently integrate and process these complicated data becomes an essential problem. In this article, we focus on the problem that analyzing variable dependencies of data collected from different edge devices in the IoT network. Because data from different devices are heterogeneous and the variable dependencies can be characterized into a graphical model, we can focus on the problem that jointly estimating multiple, high-dimensional, and sparse Gaussian Graphical Models for many related tasks (edge devices). This is an important goal in many fields. Many IoT networks have collected massive multi-task data and require the analysis of heterogeneous data in many scenarios. Past works on the joint estimation are non-distributed and involve computationally expensive and complex non-smooth optimizations. To address these problems, we propose a novel approach: Multi-FST. Multi-FST can be efficiently implemented on a cloud-server-based IoT network. The cloud server has a low computational load and IoT devices use asynchronous communication with the server, leading to efficiency. Multi-FST shows significant improvement, over baselines, when tested on various datasets.