Digital Signal Cables Penetrating a RF Shielded Room
Everything you describe sounds reasonable so far. Your 10GHz SE requirement is pretty high and typical filters for audio will never come close. Having a thermostat within the shield room is not typical however and the honeycomb ventilation (inlet &amp; exhaust) is usually sufficient for most facilities managers (best to not mention sprinkler heads). Will you be doing RF radiated immunity testing? If so you may damage the thermostat itself.

If necessary you could enclose the entire length of cable within steel conduit, run along one of the corners the room (horizontal &amp; vertical). While not perfect, the EM fields tend to be somewhat attenuated in these areas. I would be tempted to then enclose the thermostat within a metallic box that has fine mesh copper screen and bond this to the shield room walls. Finally, it can't hurt to add Low-Q ferrite beads to the cable on both ends.  You will have to select the ferrite for effectivity around the frequency(ies) of concern. Lastly, if you are concerned about the metal conduit reflecting RF signals, you can obtain ferrite tiles about 4" square and glue them in place over the conduit on a 45 degree angle in the corners.  Same goes for the thermostat box on the wall, just cover the face of the box with ferrite and leave the sides open to allow airflow.

Included with your shielding effectiveness tests, maybe you can set up an antenna and to a background ambient screen with analyzer or receiver. This will also give the emissions profile of the digital signals on the thermostat.  If in the end these cannot be eliminated, you will simply need to list these as part of the background noise every time you do any testing.