Some time ago, @Dee asked me whether the Arnia hive monitor was any good at detecting queenlessness in a hive. I haven't had a queenless state in my monitored hive since we installed the monitor, so I couldn't answer. However, I now have some related data.
Arnia recommends that you place the brood temperature probe in the middle of the brood box, as central as possible in the brood nest. The temperature should be a pretty constant 32-35C. Over the last month, the temp on our probe dropped to about 31-32C. I wasn't worried, as we are entering midwinter here in coastal California and I thought that the queen may have stopped laying, or was laying in a patchy pattern.
Last weekend, we inspected our hive which is monitored. Very interesting. During the summer, the queen tended to lay in frames 2 to 7 in our 8 frame box. Now she is laying in frames 1 to 4, all on the north side of the hive. Very odd and unpredictable. The temperature probe was between frames 4 and 5. Following the inspection, we moved it back to the center of the new brood nest, and now the temps are much more stable. Here is a screen shot:
So I think that my answer to Dee now would be that the temp probe can tell you when the brood pattern has changed, even if the hive is not queenless. I did see her during the inspection, by the way, so I know she is alive. But even more interesting to me is that the bees concentrate their effort on heating the hive laterally as well as vertically. In other words, when the queen decided to lay on the north side of the hive, the bees kept the temperature stable on that side, abandoning the south side shown by a much wider diurnal variation in temperature.