More precisely: for the US, they only checked if the “cause of death” field on the certificate mentions heat but EU statistics compare to a model of how many deaths would have occurred without a heatwave. Of course heat makes lots of indirect deadly circumastances more likely. We don’t have recent studies on heat deaths with similar methodology to compare both regions but at least the gun death statistics are more clear-cut.

Also, this is a bit cynical but people who die to heat uszally had preexisting conditions and were statistically likely to die in 10 years anyway. Meanwhile most gun deaths are young adults whose productivr careers were cut short.