Database
[{"_id":0,"temp":{"text":{"t1":{"value":"960"},"t2":{"value":"959"},"t3":{"value":"961"},"at4":{"value":"962"},"3t5":{"value":"6.0"},"j1":{"value":"3"}}}}]
Query
db.collection.aggregate([{$addFields:{"temp.text":{$arrayToObject:{$filter:{input:{$objectToArray:"$temp.text"},cond:{$regexMatch:{input:"$$this.k",regex:"t"}}}}}}}])