In order to use TemporalX you need to have a valid license which allows you to run TemporalX, and receive updates. The way licensing works with TemporalX is that you only need to have a valid license to download updates. The license will always allow you to run TemporalX for eternity on the machine it was registered to.
The registration process is quite simple, and happens the first time you run TemporalX on a machine, which is covered in the getting started documentation. Once generated, the license is limited to the OS, and hardware that were present during license registration. In certain situations due to hardware upgrades your license may become invalid for the machine it was registered on. If this happens you will need to contact support so you can be re-issued a license.
You are not required to always be online for the TemporalX license to work. The only time you need to be online is when registering the license.