Mozilla released an update to the Thunderbird 38.5.x branch on January 7th, 2016. Thunderbird 38.5.1 is for Windows users and implemented using a SHA-256 signing certificate for Windows builds, to meet new signing requirements. This was the final step of the replacing the now deprecated (as of 01/01/2016) SHA-1 signing certificates.
Windows XP SP2 users: You can not update from Thunderbird 38.4.0 (or older) to 38.5.0 automatically. You will need to manually download and install Thunderbird 38.5.0 from here and then update to the current version of Thunderbird.
Windows Vista/Server 2008 SP2 users: If you are running into issues trying to install Thunderbird 38.5.x you will need to install a Windows Update to increase the size of the GetCertHash() buffer. See this Microsoft KB for more info.
User can update from within Thunderbird via Help > About Thunderbird option or can download and manually install via the getthunderbird.com site. The next scheduled update is Thunderbird 38.6.0 in late January/early February 2016.