My advise is not Asterisk specific, but for any embedded linux distribution.
When using a thin client, you will likely be using a Disk on Module, or DOM. Think of this as a small SSD drive that is intended to boot the operating system on the device.
I actually wrote a blog post about this for pfsense. Many of the same rules will apply for Asterisk.
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www.hammerweb.com/blog/2 ··· -client/The key issue is that with any flash media, their lifespan is greatly reduced if you perform a lot of writes from the device. The best way to use these devices is simply to boot and then run from a RamDisk.
This means you will want to use a distribution specifically designed to be a for an embedded device. This generally means that writes are minimized and log files are kept in RAM.
There are two ways of getting this OS image onto the DOM module. I prefer to use a USB CD-ROM and install the OS much like you would do on any computer. However, you must delete the swap partition during the drive setup, and you will need to choose the embedded kernel during the install.
Another popular method is to use a Linux Live CD and boot into a linux environment. Then, using the 'dd' command, you copy the .img file over to the DOM.
Of course, if your thin client has a traditional HDD, then all of the above can be ignored.