Sven: My boys will stay cool.
Both men have struggled to keep their emotions in check this season, with Beckham sent off for the third time ( one of which was subsequently rescinded ( in Real Madrid's win over Getafe at the weekend.
Rooney famously blew his top in Belfast before being red-carded on Manchester United duty for stupidly applauding referee Kim Milton Nielsen during a Champions League encounter with Villarreal.
The incidents have sparked fears the duo may be targeted by unscrupulous opposition players eager to make the most of a potential weakness in an otherwise impressive side.
But Eriksson does not believe temperament will be an issue for his team in Germany next year.
"I am not worried about the temperament of Beckham or Rooney," said Eriksson. "They will do everything right at the World Cup.
"Sometimes Wayne is criticised for his behaviour on the pitch, but he has never lost his head in a big game.
"I don't believe there is a problem with David Beckham either, it is more to do with the bad run Real Madrid are having.
"They have sacked another manager, which shows something is not going right.
"David likes it at Real Madrid but the pressure there is incredible. As a coach, or a player, or a manager, you have to win and for two seasons they have not won anything."
Eriksson is approaching the tournament in bullish mood, insisting England are among half-a-dozen nations who could lift the trophy in Berlin on July 9.
He feels the lessons learned from successive quarter-final exits to Brazil and Portugal in the last two major tournaments were in evidence in the recent win over Argentina, and he is hopeful of becoming only the second coach after Sir Alf Ramsey to guide England to the ultimate success.
"If all our players hit peak form, we will be difficult to beat," he said.
"The difference between winning and losing at the last two tournaments was almost nothing and this squad, this team, is much stronger today than it was 18 months ago, let alone prior to the last World Cup.
"When you look at the voting for the best players in Europe, Frank Lampard and Steven Gerrard were in the first three.
"Then if you look at Rooney, Beckham, Michael Owen, the centre-halves, Ashley Cole and Gary Neville. We have the players who can compete with anyone in the world."