You can use Userful MultiSeat Linux. As it is specifically created for the T100/T150 thin clients. It provides extensive support and is a mature and stable choice.
Since this is a USB controlled thin client the server will at least need to have a USB driver installed for this setup to work (regardless of it's OS).
So as I was searching for information on the HP websites there was a prominent message that I could chat with support. So I talked to customer service about this issue for you. With the full transcript available here: http://pastebin.ubuntu.com/791914/
For your convenience a summary of the things I found out regarding your issue:
"Unfortunately Windows MultiPoint Server is the only operating system
this client has been tested and certified for use with, so I am not
able to guarantee that they will work with a Linux multiseat OS.
However, if there currently is a Linux multiseat server OS available,
it will likely work, although ALL functionality might not be
There are no Linux drivers from HP available for the T100 and neither are there any specification documents made publicly available to be able to write your own. The suggestion I got from them was to look into other thin clients.
"At the moment, the t5545, t5565, and t5745 thin clients fully support
both a Linux server OS and native linux client OS."
"The t5565 will be the lowest cost linux-supported model, which starts
at about $249."
To my knowledge the only way that T100 drivers can be developed without receiving the documentation from HP would be to find out the specification of it's communication protocol yourself. Considering that the setup includes the T100 hardware, to my knowledge the options of doing so only include ones that are illegal, so I would not suggest that. Besides that it's not something you can make a stable implementation of on short term.
So my next step was to give it a quick search to see if someone else already worked around this or knows something I don't know on the legal front and found that there is a Linux server available for the T100 and T150 clients. It's called Userful MultiSeat Linux. http://www2.userful.com/products/userful-multiseat-linux
It allows you to choose between a fully featured Edubuntu 10.04 installation or to use a stand-alone version to install on a distro of your choice. It has extensive information on how to set up the environment including instructional video's. And since they specifically target the T100/T150 thin clients I'm certain they have managed to include a working USB driver that was missing.
So my recommendation would be to either test this software or switch to do a clean install of it's distro version. Considering 10.04 Edubuntu is based on a LTS (Long Term Support) milestone it's a great choice for maturity and stability in an environment with poor means to get service.