This really depends on the region and the goal. For example when looking at heat wave definitions: some are constructed having 3 days a threshold exceedance of 90th percentile of the daily mean temperature, others use heat wave as being the exceedance of the 3-day running mean over a certain threshold for both daily minimum and maximum temperature. Please see the documentation provided with the application on heat wave days to learn about the different heat wave definitions we applied: http://urban-climate.copernicus-climate.eu/documents/Spells_extra_documentation.pdf For wet bulb temperature, this also depends on the region. An example study done by VITO is presented for example in this article: https://vito.be/en/news/paved-terrains-city-cause-extreme-heat-stress

Does it mean there's not a global consensus ?

I don't think so, at least not at the time I was implementing the different definitions, perhaps in the meantime things moved.

Are you aware that the atlantic council is launching a work to rank heat waves on one scale (i.e cyclones)?