It shouldn’t be too hard to do the same thing as the Yun Shield’s function, at least the core part of it, if you know a little bit about Linux scripting. But if you want the fancy web GUI, that’s more work.
First off, cron can be set up to automatically run a script daily at a designated time. (Search for Linux cron or crontab for information.)
The script can then go out over the network and fetch the compiled sketch’s .hex file from a server. You could use curl or wget to do that. (Search for Linux curl or wget for information.)
Once you have the file, compare it to the last loaded file to see if there are differences. If so, save the new file for comparison next time. (Search for Linux cmp for information)
To actually program the sketch into the '32U4 processor, make a copy of the hex file, and run:
where is the name of your temporary sketch copy. The first command will merge the Arduino bootloader with the sketch’s hex file (overwriting the original file, which is why you’re making a temporary copy) and the second command programs it into the '32U4 processor.
So, basically, you need to write a Linux shell script that fetches a new copy of the script hex file, checks to see if it is a new version, and if so, merges it with the bootloader and programs it into the processor.