Henman, the British No 1, had made Kafelnikov the first victim of his glorious run to the Wimbledon quarter-finals. But Kafelnikov proved a much sterner opponent this time and he never let Henman take charge.
The defending champion, Andre Agassi, fresh from winning the Olympic gold medal, had a slightly shaky 6-3, 2-6, 6-4 second-round victory over Sweden's Magnus Larsson.
The overwhelming heat played its part in some matches, and the only man seemingly oblivious to the conditions was the second seed, Thomas Muster, who demolished Wojtek Kowalski, a qualifier from Poland, 6-1, 6-1.
"I'm not made of steel and don't just reflect the heat or something," Muster said."I can probably just take it a little better than others."
He certainly coped better than Stefan Edberg, who wilted and surrendered a 4-0 lead in the third set as he lost 3-6, 6-4, 7-5 to the Italian Cristiano Caratti.
n Jennifer Capriati continued her resurgence as she beat fellow unseeded American Lori McNeil 7-6, 7-5 in the Canadian Women's Open in Montreal.