New Delhi, June 29 -- Every few minutes, the mortuary owner's phone rings. Since a record-smashing heat wave started taking lives and storage space for bodies in Paris and beyond, the funeral directors and mourning families calling him mostly have the same question: Do you have room for one more?

With all 32 places in his cold room taken, Zouhaeir Hertelli reluctantly has to gently say "Non," over and over and over again.

"We're facing a really catastrophic situation," he said. "I'm getting hundreds of calls."

As the historic heat wave shifted its deadly temperatures eastward this weekend to other parts of Europe, France began counting the human cost it left in its wake.

Tallying heat-related deaths could take time

The statistical an...