What kinds of gaps should one expect if each day's temperature at each location was sampled identically and independently of past years?

I don't know the exact parameters here, but mental math says that if we have data over 80 years, and we brashly pretend city temperatures are independent of each other, then the probability that any of the 400 cities exceeds its historical max on any given day is approximately 400/(80*365) ≈ 90 days, with arrivals following a Poisson train.

This expected gap can only grow if we correctly add in the positive correlation between nearby temperatures, but that will require working directly with the data. It would be nice if the website more obviously contrasted what we would see in toy models with no heating versus what we actually see in the real world.