It would be interesting to monitor the temperature to see how active it still is, since I can tell that it's not completely broken down yet. I actually have an ESP8266-based temperature sensor around here that I was using to track ambient temp for another fermentation project.
Now I'm thinking of encapsulating its thermistor and putting the 8266 in an IP67 enclosure along with a solar cell and just planting the whole lot on top of the compost pile. It already serves a web page on a .local domain so there would be minimal work required on my part.
I might actually get to that this weekend!