Have a Google for I2C temperature sensor and you should get a lot of hits. There is an exposed I2C port on the board, and with a little bit of code, you can make the clock and the sensor talk to each other.
I'm not a great fan of thermometers with Nixies: They tend to show more or less the same values for long periods, and that is not great for cathode poisoning. I'd suggest alternating the display between temperature and something else - for example pressure, as given by this module:
Switching between humidity or pressure is fine. I am gonna try to make an Steampunk Nixie Clock. If you search that on Youtube you will get an vert exclusive nixie project.
The project on the photo had 5 nixie tubes. The first one. Is that a special board, or is ir possible with your board Ian? When not connecting a 6st nixie. The tubes at the end of this video are displaying characters aswell, special tubes?
The tubes in the first (left) and last (right) positions are symbol tubes. The tube in the last position (*C) is an IN-19A. The tube in the first position is probably an IN-19B.
That board looks like it is specifically designed to be a thermometer. Ian's boards are designed to be clocks. If you wanted to use a clock board as a thermometer you would need to do some pretty serious reprogramming of the controller. Dealing with the symbol tubes could be tricky but not impossible.
Look into it later when the dust is clearing off the crater.