South Korea and Togo will play under a closed roof at Frankfurt's Commerzbank Arena on Tuesday, despite temperatures forecast to be well over 30 Celsius.
The stadium's roof structure has caused distracting shadows
Fifa have decided to close the roof to eradicate distracting shadows from the structure over the pitch, which are spoiling television images.
Director of communications Markus Siegler added: "Experts suggest it will be cooler if we provide shade."
But a leading German forecaster said: "It would be a massive greenhouse."
Siegler added that Argentina's game against Serbia and Montenegro on Friday could be played under a closed roof, saying: "We are considering the situation at Gelsenkirchen."
It would be a killer having the roof closed above
But Joerg Kachelmann, the chief meteorologist for Germany's leading ARD television station, said: "It would be a killer having the roof closed above, with the massive crowds inside.
"If they had air conditioning it would be a good idea. But without air conditioning, it would become very hot inside those stadiums."
Fans will not be allowed to take plastic bottles containing drinks into the stadiums for security reasons, while Fifa will not sanction water breaks or stoppages during games.
"Fifa is actively encouraging players to drink water, provided by Fifa and handed to the players. But it is not allowed for water bottles to be thrown on the pitch," said Siegler.