Hamilton and Nico Rosberg have secured pole in six of the past seven races, but the high temperatures forecast this weekend are expected to intensify the problems the team have had with their tyres this year.
Mercedes missed out on the chance to work with Pirelli's new range of tyres – a combination of the 2012 and 2013 designs – as they were banned from last week's young driver test at Silverstone because they took part in a rule-breaking session in Barcelona after the Spanish Grand Prix.
The team principal, Ross Brawn, admitted Mercedes were on the back foot when he said: "Both Nico and Lewis have visited the factory in the two weeks since we returned from Germany and everyone has been working very hard to investigate our tyre sensitivities ahead of the elevated temperatures we will undoubtedly experience this weekend in Budapest.
"Friday will also be our first opportunity to work with the new tyres on our car, so we have a great deal to learn in a short space of time. We want to finish the first half of the season on a high, but the challenge facing us is clear. The final race before the summer break is always a milestone for the team and an opportunity to review our performance before our staff enjoy a well-deserved break during the summer shutdown.
"Our team are currently second in the constructors' championship with two race wins to date. However, the season has not been without its challenges and we have had some very tough races."
Meanwhile, the Lotus team principal, Eric Boullier, says he is battling not to lose his leading driver Kimi Raikkonen to Red Bull, where the Finn is expected to replace Mark Webber next year.
Boullier said: "Lotus is a desirable place to be. We know there's been a lot of talk about Kimi's future, and we all know Kimi is an individual and he will make his decision in his own time. Naturally, we want him to continue in the sport and continue with Lotus, so we're doing everything we can do to make that happen."
There is another battle going on in Formula One away from the track – this time to stop Jean Todt winning a second term as the FIA president.
There is a lot of resentment in the paddock towards Todt – it is perceived that there is a lack of leadership in the sport and that the decision to return to Bahrain was a disaster.
Now there could be a challenge from David Ward, one of former president Max Mosley's key aids and the boss of the FIA Foundation road safety organisation since 2011. He said: "This is not what I intended nor what I wanted, but I am certainly thinking about [standing] because it is important to have a debate."
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