Steven,
Our practice is located in Texas. We store and administer state vaccines. I'm not sure what the exact wording of the Texas requirement is for the thermometer, but our setup puts us in compliance. We have the same setup as Donna: fluid filled bottles with wires that run to an external digital thermometer with continuous output and high/low alarms.
We found out about these thermometers through the Texas Vaccines For Children (TFVC) program. I think you should ask your state vaccine agency how other practices comply.
Mario.