Going out on a limb here – since I’m not familiar with the specific product, but am in general.
You didn’t specify, but I’m assuming that you mean one of the Wyse Winterm thin clients. A quick search of the Wyse support web site (wyse.com AskWyse.com) indicates that these systems are usually managed with a package called Rapport. Do you know if your company uses that?
The other possibility is that they get their IP address through DHCP, either industry standard or some Wyse extensions.
Sorry not to be of more help, but hopefully that points you in the right direction.