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 add-on, you need to set up the URL to JIRA and the log in 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 a 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.