The 12th-seeded German need 10 match points and two-and-three-quarter hours before winning 12-10 in the final set tie-break in a 2-6, 6-4, 7- 6 victory over the American Paul Goldstein to earn a meeting with the British No 1.
Kiefer finished at 10.30pm, leaving him 16 hours in which to recover to play Henman, who had a rest day after beating the Dutchman John Van Lottum on Tuesday.
"But Kiefer's been playing well lately and will be difficult," warned Henman, aware that he has lost twice in three matches to the young German.
The order of play yesterday meant that Henman will avoid playing under the floodlights, which have bothered some players, but he will have to endure the afternoon heat.
The temperature can rise to 90F in the shade and Henman's fitness, much improved in the past two years with the help of his trainer, Tim Newham, may be an important factor.
Henman is desperate to do well, having suffered two defeats in two matches in the past two weeks and with the US Open little more than a fortnight away.
"It was a relief to get a win under my belt," he admitted after a 6-2, 6-1 victory over Van Lottum on Tuesday which was his first since Wimbledon.
If Henman wins again he could intervene in a tussle for the world No 1 spot, for he is seeded for a quarter-final with the Russian Yevgeny Kafelnikov.
Kafelnikov, who beat Sweden's Jonas Bjorkman, 6-1, 6-4, can regain the top position from Pete Sampras, who had to save three set points before overcoming Jan Siemerink of the Netherlands, 7-6, 6-4.
Pat Rafter, meanwhile, ignored hot air balloons, a light aircraft and a flight of geese on Wednesday night to pound out a 7-6, 6-3 win over Daniel Vacek.
Rafter, who won this title last year before going on to win his second successive US Open championship, remained focused against the Czech player despite the interruptions from the air.
At one point in the first set it appeared that an invasion from the skies was imminent as two balloons took off on the tournament grounds and flew over the stadium. Seconds later a small plane all but "buzzed" the stadium.
However, the Australian shook off the distractions to keep his preparations for Flushing Meadow firmly on track.
There were also wins for the French Open champion, Andre Agassi, and Michael Chang.
Agassi earned his 17th victory in 18 matches against French players by defeating Arnaud Di Pasquale, 6-4, 6-1, in just under an hour, while Chang, once ranked second in the world, showed his fighting qualities to knock out the No 8 seed, Alex Corretja of Spain, 6-3, 6-7, 6-2.Reuse content