I recently came across this paper and found it helpful.
Jiang, Bin. (2012). Head/tail Breaks: A New Classification Scheme for Data with A Heavy-Tailed Distribution. Professional Geographer - PROF GEOGR. 65. 10.1080/00330124.2012.700499.
The closest solution I can think of all requires you to divide your data into specific time periods, rather than computing the time range separately for each hotspot.
If that's acceptable, it's actually quite simple to do.
Decide on some time periods, Eg [Jan-Feb 1999, Mar-Apr 1999, May-Jun 1999, ...]
Add a new "time_period" field to the layer, using the ...
Building off of genorama's answer above, you can also convert the output of bkde2D into a raster rather than contour lines, using the fhat values as the raster cell values
inurl <- "https://data.cityofchicago.org/api/...