This post was inspired by this week's rather tepid four-day heat wave (Aug. 5-8, 2018), which had an average high of 90.8 degrees (with highs of 91, 92, 90 and 90). Of the 66 four-day heat waves that have occurred since 1870 only one, in July 1896, had a lower average high, 90.3 degrees. (2018's low-grade heat wave matched one in August 2009.) On average, four-day heat waves have had an average high close to 94°. (The hottest four-day heat wave on record took place in the summer of 2010, when the high temperature from July 4-7 was 99.5°.)
However, the story changes when low temperatures are included in the analysis. For example, this August's heat wave had an average low of 75.0 degrees, which was 1.3 degrees warmer than the average four-day streak and warmer than two-thirds of the four-day heat waves examined. When combined with the average high, the mean temperature ranked as 27th coolest - quite a difference in ranking compared to its average high alone. (This follows the weather storyline of this century whereby nighttime temperatures in New York are warming more than daytime temperatures.)
Finally, while the typical four-day heat wave had a 20-degree difference between its high and low, this August's was 15.8 degrees apart, which was the third smallest diurnal variation of the heat waves studied (a heat wave in July 1995 had the smallest, 14.7 degrees, while the second smallest was in July 1870).