Thunderbird Integration for JIRA is is able to create JIRA issues out of emails or add the content of an email as a comment on an issue. After the installation of the plug in you need to setup the URL to JIRA and the login credentials in the preferences dialog of the Thunderbird extension. On a right click on an email you now will see two new items in the context menu: "Create JIRA Issue" and "Add as JIRA comment". When you select one of them a new dialog window will open.

Thunderbird Integration for JIRA works on JIRA server and JIRA cloud.