I don't believe they did. The suspicion is that Philip IV of France owed the Templars so much money that he got rid of them on a trumped up charge. Similar actions were taken against Lombards and Jews by other rulers when they realised they couldn't get out of their debts by any other means. The Knights Hospitaller (Order of St John of Jerusalem) were unaffected by the purge of the Templars (indeed they accepted many of the former Templars as members) and went on until the early 19th century (I think) although by the end they were an organisation much reduced in power. After the Battle of Lepanto the main need for them had disappeared. The Templars were always a problem for mediaeval rulers - owing more allegiance to God and the Order than to any King was a recipe for distrust.
There are a couple of distinctly modern organisations with the word Temple or Templar in their title but they have absolutely no connection with the original Order.