Once downloaded, open Tools | Add-ons, and drag and drop the .xpi file on your add-ons tab. No need to restart Thunderbird.
The profiler extension will show up in the bottom right of the status bar with two small panels labeled 'Disabled', and 'Dump Profile'.
Remember to disable or uninstall the extension when not using it. Performance is affected while the extension is enabled and gathering data.
Using the profiler
Click on 'Disabled' to switch the profiler into enabled mode. When "Enabled", the profiler is recording data.
Reproduce the performance problem 5-15 seconds. But do not run longer, because the profile may be too big to upload to the server.
Click on 'Dump Profile'.
A content tab like the screen below will show you profiling data gathered up to that point.
Click on 'Enabled' to stop data gathering. The label will change to Disabled.
Click the 'Share' button in the bottom left. This will upload the profile data and once completed will write out a link.
Copy this URL to your clipboard by right clicking. Paste the profile URL in your bug bug report or email to the appropriate person. Give some context, with details about what you were doing to cause the performance problem. For example, scrolling the message list.