T-Mobile is pushing out an update to the Galaxy Note 3 today that will either enable VoLTE service on the device, or update the device to the most recent Android version/baseband. The Android version update is the smaller of the two software upgrades that Note 3 owners on Big Magenta's network are likely being notified about, and after being downloaded and installed those users will have their Note 3 devices updated to Android 4.2.2/Baseband N900TUVUDNF4. Users will only be getting this update pushed out to them over the air if they had already received, and had installed the larger file size update to enable the device for VoLTE, which was initially sent out prior to now sometime last month.
Those who are not already enabled for VoLTE service and are in one of the supported markets, may want to initialize the update and make sure to install it as they will end up getting faster data speeds. The file size is quite a bit larger however so users will certainly want to make sure that they have a very healthy amount of battery life before proceeding with the process. T-mobile also mentions that users who will be needing to do this update will have to proceed with requesting the update through WiFi because of the fact that it is a huge file, about 188MB. That is a larger than normal software update than we usually see from carriers.
Users will also have the option to download the update file and install it via the Samsung Kies software manually, which will be available today as well. As for when the OTA updates will start hitting devices, that has already begun but it's likely that not everyone will see the update pop up in their status bars today. Those who have the larger file update to install will have to go into settings and manually search for it anyway, so just make sure you're checking periodically. T-Mobile was mostly vague about what the update includes, short of stating it brings improvements and the Download Booster feature to the device that we had already seen on the T-Mobile Galaxy S5.