Those who are using Thesis theme, they know that Thesis customization is mostly done by custom.css and custom functions.php file located in custom Thesis folder. When ever we talk about taking a back up or upgrading Thesis, we suggest you to take a complete back up of custom folder by downloading it locally. Though this is not the only backup which you need, but you might have made some changes from Thesis site option and Thesis design option to customize your Thesis theme.
If you are planning to take back up of your customized thesis theme, along with taking back up of custom folder, you need to take back of Thesis settings. In latest version of Thesis, you can always import and export settings from Thesis option manager. This is located in the option menu of Thesis theme and you can take back up of individual settings or all options at once.
See the screenshot to understand where you can find this setting to take backup:
Here is a short video tutorial to understand how you can take Thesis theme backup of site and design option:
Do let us know if you have any query regarding Thesis theme. You can also get in touch with us for Thesis Customization Service.