As a ubiquitous form of data in the natural world, time has been widely used in many domains such as the military, finance, medical treatment, and environment. Temporal data models that are used to model the dynamic development process of data are constantly proposed, such as temporal database and temporal XML. With the rapid development and popularization of the Web, the requirement of dealing with diverse data efficiently is becoming more important. As a new generation of data exchange language, JSON (JavaScript Object Notation) has been widely used because it is lightweight, has fast parsing, and has high transmission efficiency. In this paper, we propose a novel temporal JSON data model. Based on the proposed temporal JSON data model, we further propose two temporal JSON query languages, t-JSONPath, and t-JSONiq, which are the temporal extensions to JSONPath and JSONiq, respectively. With the proposed temporal JSON data model, we demonstrate our temporal JSON query languages with typical temporal query examples and evaluate their query response times.