After setting Friday's fastest second practice time at the Nurburgring a bullish Hamilton predicted a brighter future for the McLaren MP4-24.
Ferrari's Kimi Raikkonen was running with the new front wing that helped team-mate Felipe Massa get onto the podium at the Nurburgring.
After stringing together four back-to-back victories between Bahrain and Turkey, Button has seen his momentum falter, finishing sixth in Britain and fifth at the Nurburgring.
McLaren driver Kimi Raikkonen starts Sunday's European Grand Prix at the Nurburgring on pole position and is just three points adrift of Ferrari's world champion Michael Schumacher.
Brawn opted for a three-stop strategy for Button and Barrichello at the Nurburgring, but the Brazilian's race was disrupted by a problem with the fuel hose during his second stop.
When his all-action style comes off, like passing Michael Schumacher around the outside of the downhill hairpin at the Nurburgring in June, the wow factor has the grandstands on their feet.
BBC: SPORT | Motorsport | Formula One | Schumacher one step away
But seven-time world champion Schumacher has won a record 91 grands prix and it's no surprise the 43-year-old managed four of those at Hockenheim, plus five victories when the European Grand Prix was held at the Nurburgring.
But after the FIA put out a lengthy statement on Thursday detailing its side of the argument, the bosses of the Fota teams were taking a more conciliatory line as they arrived at the Nurburgring ahead of Sunday's German Grand Prix.
But the team principal's pleasure at Schumacher's transformation from woodentop to winner after the Nurburgring and Magny-Cours did not disguise the force of the team's earlier frustration.
But Schumacher, who has won the European Grand Prix a record six times at its former homes in Jerez and Nurburgring, is confident Mercedes can overcome the reliability issues which have dogged him.
German media also reported that Guenther Oettinger, premier of the southern state of Baden-Wuerttemberg, had canceled a meeting with the Briton at this weekend's German Grand Prix at Nurburgring because of his comments about Hitler.
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