I am perfectly comfortable (and therefore want my system to turn off) after my AC has been running long enough to drop the humidity a bit, even if the temp has only dropped a fraction of a degree. As humid air leaks in, I want the AC back on even if the temp has barely increased a degree. Basically the heat index in my house swings enough to change my comfort and therefore could be a useful trigger, even if the temperature doesn't swing nearly enough to be a useful trigger.
The Nest even has a humidity sensor, but it only gets used in very specific (hardly useful) situations.
I considered writing a Works With Nest app for this. Then that platform disappeared in favor of Works With Google, but I never found the time for either...
You could try wrapping your thermostat in a wet sock.
Actual web-bulb thermometers would either require manually adding water when you want to make a measurement, or have a large tank of water that gets continuously wicked onto a cloth which is wrapped around the thermometer. The general idea is that, if the surrounding air is dry, the water in the cloth will evaporate and cool the thermometer below the temperature of the air itself (the "dry-bulb temperate"). This is just the same evaporative cooling effect that makes sweating and swamp coolers work. If the surrounding air is very wet (humid), very little evaporate cooling will occur, and the wet-bulb temperature will be very close to the dry-bulb temperature.
I'm not sure how well a thermostat that only used the wet-bulb temperature would work. To actually calculate relative humidity, you would need at least a wet-bulb and dry-bulb measurement. But given that relative humidity in most places probably doesn't swing that wildly, I imagine that just finding a comfortable wet-bulb temperate for your thermostat might work okay in practice.
Rigging a wet sock (with constant wicking from a water source) onto my actual wall-mounted Nest Thermostat would never fly, as I said, but I have no qualms about doing this experiment with my Nest Temperature Sensor, being a small and relatively cheap thing that I can easily steal for a while...
According to a psychrometric chart [0] it looks like if the dry-bulb temperature stays locked at 70F, while the RH drops from 60% to 40%, the wet-bulb temperature will drop from 62F to 56F. Or if the dry-bulb temperature stays locked at 80F while the RH drops as before, the wet-bulb temperature will drop from 70F to 64F. That's linear enough for my purposes.
Therefore if my conventional (dry-bulb) set point is 75F in the summer, and I'm most comfortable around 50% RH combined with that 75F, then I'll try a set point of 63F with my Nest using the remote Sensor wrapped in wet cloth!
Apparently I also need continuous airflow over this wet-bulb thermometer. I wonder how much.
[0] https://hvacologist.com/2022/02/21/wet-bulb-temperature-vs-d...
When I get back from a run in August at near heatstroke levels I will almost never cool down if it's not set on the "chilly" side. Conversely, in winter when heatstroke is replaced with near frostbite I am chilled to the core and need much higher heat to ever warm up.