Time-varying JSON data are being used and exchanged in a lot of today's application frameworks like IoT platforms, Web services, cloud computing, online social networks, and mobile systems. However, in the state-of-the-art of JSON data management, there is neither a consensual nor a standard language for updating (i.e., inserting, modifying, and deleting) temporal JSON data, like the TSQL2 or SQL:2016 language for temporal relational data. Moreover, existing JSON-based NoSQL DBMSs (e.g., MongoDB, Couchbase, CouchDB, OrientDB, and Riak) and both commercial DBMSs (e.g., IBM DB2 12, Oracle 19c, and MS SQL Server 2019) and open-source ones (e.g., PostgreSQL 15, and MySQL 8.0) do not provide any support for maintaining temporal JSON data. Also in our previously proposed temporal JSON framework, called τ JSchema, there was no feature for temporal JSON instance update. For these reasons, we propose in this paper a temporal update language, named τ JUpdate (Temporal JUpdate), for JSON data in the τ JSchema environment. We dene it as a temporal extension of our previously introduced non-temporal JSON update language, named JUpdate (JSON Update). Both the syntax and the semantics of the data modication operations of JUpdate have been extended to support temporal aspects. τ JUpdate allows (i) to specify temporal JSON updates in a user-friendly manner, and (ii) to eciently execute them.